Probability Problems

Probability Problems

Do you want to know how to solve Probability Problems? Here you learn how to solve probability word problems.

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

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

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

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. \(\color{blue}{\frac{7}{25}}\)
  6. \(\color{blue}{\frac{9}{25}}\)

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