Probability worksheet with answers

Free printable Probability worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
red: 7blue: 6green: 3

A bag holds 7 red, 6 blue and 3 green balls. You draw one at random. What is the probability P that it is blue?

7 / 6 / 3
P =
2.Easy
xp(x)10.3520.130.340.25

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 1, 2, 3, 4p(x): 0.35, 0.1, 0.3, 0.25
E(X) =
3.Medium
n = 8k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 8? The order does not matter.

n = 8k = 3
N =
4.Medium
n = 14k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 14? The order does not matter.

n = 14k = 3
N =
5.Hard
n = 5, p = 0.4: P(X ≤ 1) = ?k012345

5 components are tested, and each one fails with probability 0.4, independently. What is the probability P that at most one fails?

n = 5p = 0.4
P =
6.Hard
n = 11, p = 0.7: P(X ≤ 1) = ?k01234567891011

11 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 11p = 0.7
P =

Answer key

  1. 1. P = 0.375
  2. 2. E(X) = 2.45
  3. 3. N = 56
  4. 4. N = 364
  5. 5. P = 0.337
  6. 6. P = 4.724 × 10⁻⁵

Full step-by-step solutions: practise this topic on examproblems.com.