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: \(\frac{number\ of \ favorable \ outcome}{total \ number \ of \ possible \ outcomes}\)

Probability Problems For education statistics and research, visit the National Center for Education Statistics.

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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

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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