How to Solve Probability Problems? (+FREE Worksheet!)

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Step by step guide to solve Probability Problems

• Probability is the likelihood of something happening in the future. It is expressed as a number between zero (can never happen) to $1$ (will always happen).
• Probability can be expressed as a fraction, a decimal, or a percent.
• To solve a probability problem identify the event, find the number of outcomes of the event, then use probability law: $\frac{number\ of \ favorable \ outcome}{total \ number \ of \ possible \ outcomes}$

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Probability Problems – Example 1:

If there are $8$ red balls and $12$ blue balls in a basket, what is the probability that John will pick out a red ball from the basket?

Solution:

There are $8$ red balls and $20$ a total number of balls. Therefore, the probability that John will pick out a red ball from the basket is $8$ out of $20$ or $\frac{8}{8+12}=\frac{8}{20}=\frac{2}{5}$.

Probability Problems – Example 2:

A bag contains $18$ balls: two green, five black, eight blue, a brown, a red, and one white. If $17$ balls are removed from the bag at random, what is the probability that a brown ball has been removed?

Solution:

If $17$ balls are removed from the bag at random, there will be one ball in the bag.
The probability of choosing a brown ball is $1$ out of $18$. Therefore, the probability of not choosing a brown ball is $17$ out of $18$ and the probability of having not a brown ball after removing $17$ balls is the same.

Exercises for Solving Probability Problems

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Solve.

1. A number is chosen at random from $1$ to $10$. Find the probability of selecting a $4$ or smaller.
2. A number is chosen at random from $1$ to $50$. Find the probability of selecting multiples of $10$.
3. A number is chosen at random from $1$ to $10$. Find the probability of selecting of $4$ and factors of $6$.
4. A number is chosen at random from $1$ to $10$. Find the probability of selecting a multiple of $3$.
5. A number is chosen at random from $1$ to $50$. Find the probability of selecting prime numbers.
6. A number is chosen at random from $1$ to $25$. Find the probability of not selecting a composite number.

Download Probability Problems Worksheet

1. $\color{blue}{\frac{2}{5}}$
2. $\color{blue}{\frac{1}{10}}$
3. $\color{blue}{\frac{1}{2}}$
4. $\color{blue}{\frac{3}{10}}$
5. $\color{blue}{\frac{3}{10}}$
6. $\color{blue}{\frac{9}{25}}$

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