What is the probability that the coin will land on Heads?
Solution & Explanation
Let's figure out the probability of landing on Heads! 📌
Step 1: Identify all possible outcomes.
When you flip a coin, there are two possible outcomes: Heads or Tails.
Step 2: Identify the favorable outcome.
We want the coin to land on Heads, so there is 1 favorable outcome.
Step 3: Calculate the probability.
Probability is calculated as:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\]
In this case:
\[
\text{Probability (Heads)} = \frac{1}{2}
\]
✅ So, the probability of the coin landing on Heads is \( \frac{1}{2} \).
2
Solved Example
Easy Level
🎲 Sarah rolls a standard six-sided number cube (dice) once. The sides are numbered 1, 2, 3, 4, 5, and 6.
What is the probability that Sarah rolls an even number?
Solution & Explanation
Let's find the probability of rolling an even number! 👉
Step 1: List all possible outcomes.
When rolling a standard number cube, the possible outcomes are {1, 2, 3, 4, 5, 6}. There are 6 total possible outcomes.
Step 2: List the favorable outcomes (even numbers).
The even numbers on the cube are {2, 4, 6}. There are 3 favorable outcomes.
Step 3: Calculate the probability.
\[
\text{Probability (Even Number)} = \frac{\text{Number of even numbers}}{\text{Total number of outcomes}} = \frac{3}{6}
\]
This fraction can be simplified.
\[
\frac{3}{6} = \frac{1}{2}
\]
✅ The probability of rolling an even number is \( \frac{1}{2} \).
3
Solved Example
Medium Level
🎒 In a bag, there are 4 red marbles, 3 blue marbles, and 5 yellow marbles.
If you pick one marble from the bag without looking, what is the probability that it will be a blue marble?
Solution & Explanation
Let's calculate the probability of picking a blue marble! 🔵
Step 1: Find the total number of possible outcomes.
Add the number of all marbles in the bag:
\( 4 \text{ (red)} + 3 \text{ (blue)} + 5 \text{ (yellow)} = 12 \text{ marbles} \)
So, there are 12 total possible outcomes.
Step 2: Identify the number of favorable outcomes.
We want to pick a blue marble. There are 3 blue marbles in the bag. So, there are 3 favorable outcomes.
Step 3: Calculate the probability.
\[
\text{Probability (Blue Marble)} = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{3}{12}
\]
This fraction can be simplified.
\[
\frac{3}{12} = \frac{1}{4}
\]
✅ The probability of picking a blue marble is \( \frac{1}{4} \).
4
Solved Example
Medium Level
🎨 A spinner is divided into different colored sections. There are 2 red sections, 3 blue sections, and 1 yellow section.
Which color is the spinner most likely to land on? Which color is it least likely to land on?
Solution & Explanation
Let's analyze the likelihood of the spinner landing on each color! 🎯
Step 1: Find the total number of sections.
Add the number of sections for each color:
\( 2 \text{ (red)} + 3 \text{ (blue)} + 1 \text{ (yellow)} = 6 \text{ sections} \)
There are 6 total sections.
Step 2: Determine the probability for each color.
Probability (Red): \( \frac{2}{6} \)
Probability (Blue): \( \frac{3}{6} \)
Probability (Yellow): \( \frac{1}{6} \)
Step 3: Compare the probabilities to find most and least likely.
The color with the highest probability is the most likely, and the color with the lowest probability is the least likely.
Comparing the fractions: \( \frac{3}{6} \) is the largest, and \( \frac{1}{6} \) is the smallest.
✅ The spinner is most likely to land on Blue (probability \( \frac{3}{6} \)).
✅ The spinner is least likely to land on Yellow (probability \( \frac{1}{6} \)).
5
Solved Example
Real World Example
🍎 Sarah's lunchbox has 2 apples, 3 bananas, and 1 orange.
If she reaches into her lunchbox without looking and picks one fruit, what is the probability that she picks an apple?
Solution & Explanation
Let's find the probability of Sarah picking an apple! 🍏
Step 1: Find the total number of fruits.
Add the number of all fruits in the lunchbox:
\( 2 \text{ (apples)} + 3 \text{ (bananas)} + 1 \text{ (orange)} = 6 \text{ fruits} \)
So, there are 6 total possible outcomes.
Step 2: Identify the number of favorable outcomes.
We want Sarah to pick an apple. There are 2 apples. So, there are 2 favorable outcomes.
Step 3: Calculate the probability.
\[
\text{Probability (Apple)} = \frac{\text{Number of apples}}{\text{Total number of fruits}} = \frac{2}{6}
\]
This fraction can be simplified.
\[
\frac{2}{6} = \frac{1}{3}
\]
✅ The probability that Sarah picks an apple is \( \frac{1}{3} \).
6
Solved Example
Medium Level
🔢 You have a set of 10 cards, numbered from 1 to 10.
If you pick one card randomly, what is the probability that the number on the card is greater than 7?
Solution & Explanation
Let's determine the probability of picking a card with a number greater than 7! 🃏
Step 1: List all possible outcomes.
The cards are numbered {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. There are 10 total possible outcomes.
Step 2: List the favorable outcomes (numbers greater than 7).
The numbers greater than 7 are {8, 9, 10}. There are 3 favorable outcomes.
Step 3: Calculate the probability.
\[
\text{Probability (Number > 7)} = \frac{\text{Number of outcomes greater than 7}}{\text{Total number of outcomes}} = \frac{3}{10}
\]
✅ The probability of picking a card with a number greater than 7 is \( \frac{3}{10} \).
7
Solved Example
Real World Example
🎟️ For a school raffle, 50 tickets were sold. You bought 5 of those tickets.
What is the probability that you win a prize?
Solution & Explanation
Let's calculate your chances of winning the raffle! 🎉
Step 1: Find the total number of possible outcomes.
The total number of tickets sold is 50. So, there are 50 total possible outcomes (any ticket could be chosen).
Step 2: Identify the number of favorable outcomes.
You bought 5 tickets, so there are 5 favorable outcomes (any of your 5 tickets could win).
Step 3: Calculate the probability.
\[
\text{Probability (You Win)} = \frac{\text{Number of tickets you bought}}{\text{Total number of tickets sold}} = \frac{5}{50}
\]
This fraction can be simplified.
\[
\frac{5}{50} = \frac{1}{10}
\]
✅ The probability that you win a prize is \( \frac{1}{10} \).
8
Solved Example
Medium Level
For each event below, decide if it is Impossible, Unlikely, Equally Likely, Likely, or Certain.
The sun will rise tomorrow.
You will roll a 7 on a standard six-sided number cube.
You flip a coin and it lands on heads.
It will snow in Florida in July.
You will pick a red marble from a bag with 9 red marbles and 1 blue marble.
Solution & Explanation
Let's classify each event based on its probability! 🤔
1. The sun will rise tomorrow.
This is an event that is expected to happen without fail.
👉 Certain
2. You will roll a 7 on a standard six-sided number cube.
A standard six-sided number cube only has numbers 1 through 6. Rolling a 7 is not possible.
👉 Impossible
3. You flip a coin and it lands on heads.
When flipping a fair coin, there are two outcomes (Heads or Tails), and each has an equal chance of happening (\( \frac{1}{2} \)).
👉 Equally Likely
4. It will snow in Florida in July.
Florida is a warm state, and July is typically its hottest month. While not entirely impossible, it is extremely rare.
👉 Unlikely
5. You will pick a red marble from a bag with 9 red marbles and 1 blue marble.
There are 10 marbles total. The probability of picking red is \( \frac{9}{10} \), which is very high.
👉 Likely
5th Grade Math: Probability Practice Questions
Example 1:
💡 Imagine you flip a fair coin one time.
What is the probability that the coin will land on Heads?
Solution:
Let's figure out the probability of landing on Heads! 📌
Step 1: Identify all possible outcomes.
When you flip a coin, there are two possible outcomes: Heads or Tails.
Step 2: Identify the favorable outcome.
We want the coin to land on Heads, so there is 1 favorable outcome.
Step 3: Calculate the probability.
Probability is calculated as:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\]
In this case:
\[
\text{Probability (Heads)} = \frac{1}{2}
\]
✅ So, the probability of the coin landing on Heads is \( \frac{1}{2} \).
Example 2:
🎲 Sarah rolls a standard six-sided number cube (dice) once. The sides are numbered 1, 2, 3, 4, 5, and 6.
What is the probability that Sarah rolls an even number?
Solution:
Let's find the probability of rolling an even number! 👉
Step 1: List all possible outcomes.
When rolling a standard number cube, the possible outcomes are {1, 2, 3, 4, 5, 6}. There are 6 total possible outcomes.
Step 2: List the favorable outcomes (even numbers).
The even numbers on the cube are {2, 4, 6}. There are 3 favorable outcomes.
Step 3: Calculate the probability.
\[
\text{Probability (Even Number)} = \frac{\text{Number of even numbers}}{\text{Total number of outcomes}} = \frac{3}{6}
\]
This fraction can be simplified.
\[
\frac{3}{6} = \frac{1}{2}
\]
✅ The probability of rolling an even number is \( \frac{1}{2} \).
Example 3:
🎒 In a bag, there are 4 red marbles, 3 blue marbles, and 5 yellow marbles.
If you pick one marble from the bag without looking, what is the probability that it will be a blue marble?
Solution:
Let's calculate the probability of picking a blue marble! 🔵
Step 1: Find the total number of possible outcomes.
Add the number of all marbles in the bag:
\( 4 \text{ (red)} + 3 \text{ (blue)} + 5 \text{ (yellow)} = 12 \text{ marbles} \)
So, there are 12 total possible outcomes.
Step 2: Identify the number of favorable outcomes.
We want to pick a blue marble. There are 3 blue marbles in the bag. So, there are 3 favorable outcomes.
Step 3: Calculate the probability.
\[
\text{Probability (Blue Marble)} = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{3}{12}
\]
This fraction can be simplified.
\[
\frac{3}{12} = \frac{1}{4}
\]
✅ The probability of picking a blue marble is \( \frac{1}{4} \).
Example 4:
🎨 A spinner is divided into different colored sections. There are 2 red sections, 3 blue sections, and 1 yellow section.
Which color is the spinner most likely to land on? Which color is it least likely to land on?
Solution:
Let's analyze the likelihood of the spinner landing on each color! 🎯
Step 1: Find the total number of sections.
Add the number of sections for each color:
\( 2 \text{ (red)} + 3 \text{ (blue)} + 1 \text{ (yellow)} = 6 \text{ sections} \)
There are 6 total sections.
Step 2: Determine the probability for each color.
Probability (Red): \( \frac{2}{6} \)
Probability (Blue): \( \frac{3}{6} \)
Probability (Yellow): \( \frac{1}{6} \)
Step 3: Compare the probabilities to find most and least likely.
The color with the highest probability is the most likely, and the color with the lowest probability is the least likely.
Comparing the fractions: \( \frac{3}{6} \) is the largest, and \( \frac{1}{6} \) is the smallest.
✅ The spinner is most likely to land on Blue (probability \( \frac{3}{6} \)).
✅ The spinner is least likely to land on Yellow (probability \( \frac{1}{6} \)).
Example 5:
🍎 Sarah's lunchbox has 2 apples, 3 bananas, and 1 orange.
If she reaches into her lunchbox without looking and picks one fruit, what is the probability that she picks an apple?
Solution:
Let's find the probability of Sarah picking an apple! 🍏
Step 1: Find the total number of fruits.
Add the number of all fruits in the lunchbox:
\( 2 \text{ (apples)} + 3 \text{ (bananas)} + 1 \text{ (orange)} = 6 \text{ fruits} \)
So, there are 6 total possible outcomes.
Step 2: Identify the number of favorable outcomes.
We want Sarah to pick an apple. There are 2 apples. So, there are 2 favorable outcomes.
Step 3: Calculate the probability.
\[
\text{Probability (Apple)} = \frac{\text{Number of apples}}{\text{Total number of fruits}} = \frac{2}{6}
\]
This fraction can be simplified.
\[
\frac{2}{6} = \frac{1}{3}
\]
✅ The probability that Sarah picks an apple is \( \frac{1}{3} \).
Example 6:
🔢 You have a set of 10 cards, numbered from 1 to 10.
If you pick one card randomly, what is the probability that the number on the card is greater than 7?
Solution:
Let's determine the probability of picking a card with a number greater than 7! 🃏
Step 1: List all possible outcomes.
The cards are numbered {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. There are 10 total possible outcomes.
Step 2: List the favorable outcomes (numbers greater than 7).
The numbers greater than 7 are {8, 9, 10}. There are 3 favorable outcomes.
Step 3: Calculate the probability.
\[
\text{Probability (Number > 7)} = \frac{\text{Number of outcomes greater than 7}}{\text{Total number of outcomes}} = \frac{3}{10}
\]
✅ The probability of picking a card with a number greater than 7 is \( \frac{3}{10} \).
Example 7:
🎟️ For a school raffle, 50 tickets were sold. You bought 5 of those tickets.
What is the probability that you win a prize?
Solution:
Let's calculate your chances of winning the raffle! 🎉
Step 1: Find the total number of possible outcomes.
The total number of tickets sold is 50. So, there are 50 total possible outcomes (any ticket could be chosen).
Step 2: Identify the number of favorable outcomes.
You bought 5 tickets, so there are 5 favorable outcomes (any of your 5 tickets could win).
Step 3: Calculate the probability.
\[
\text{Probability (You Win)} = \frac{\text{Number of tickets you bought}}{\text{Total number of tickets sold}} = \frac{5}{50}
\]
This fraction can be simplified.
\[
\frac{5}{50} = \frac{1}{10}
\]
✅ The probability that you win a prize is \( \frac{1}{10} \).
Example 8:
For each event below, decide if it is Impossible, Unlikely, Equally Likely, Likely, or Certain.
The sun will rise tomorrow.
You will roll a 7 on a standard six-sided number cube.
You flip a coin and it lands on heads.
It will snow in Florida in July.
You will pick a red marble from a bag with 9 red marbles and 1 blue marble.
Solution:
Let's classify each event based on its probability! 🤔
1. The sun will rise tomorrow.
This is an event that is expected to happen without fail.
👉 Certain
2. You will roll a 7 on a standard six-sided number cube.
A standard six-sided number cube only has numbers 1 through 6. Rolling a 7 is not possible.
👉 Impossible
3. You flip a coin and it lands on heads.
When flipping a fair coin, there are two outcomes (Heads or Tails), and each has an equal chance of happening (\( \frac{1}{2} \)).
👉 Equally Likely
4. It will snow in Florida in July.
Florida is a warm state, and July is typically its hottest month. While not entirely impossible, it is extremely rare.
👉 Unlikely
5. You will pick a red marble from a bag with 9 red marbles and 1 blue marble.
There are 10 marbles total. The probability of picking red is \( \frac{9}{10} \), which is very high.
👉 Likely