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: 5blue: 8green: 3

A bag holds 5 red, 8 blue and 3 green balls. You draw one at random. What is the probability P that it is not red?

5 / 8 / 3
P =
2.Easy
red: 2blue: 6green: 4

A bag holds 2 red, 6 blue and 4 green balls. You draw one at random. What is the probability P that it is not red?

2 / 6 / 4
P =
3.Medium
xp(x)100.1200.35300.3400.25μ = 27

For the distribution shown, find the standard deviation σ of X.

x: 10, 20, 30, 40p(x): 0.1, 0.35, 0.3, 0.25
σ =
4.Medium
xp(x)00.310.3520.35μ = 1.05

For the distribution shown, find the variance Var(X) of X.

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
Var(X) =
5.Hard
n = 10, p = 0.7: P(X = 1) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 1 correct answers?

n = 10p = 0.7k = 1
P =
6.Hard
n = 12, p = 0.4: P(X ≤ 1) = ?k0123456789101112

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

n = 12p = 0.4
P =

Answer key

  1. 1. P = 0.6875
  2. 2. P = 0.8333
  3. 3. σ = 9.539
  4. 4. Var(X) = 0.6475
  5. 5. P = 0.0001378
  6. 6. P = 0.01959

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