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: 8blue: 7

A bag holds 8 red and 7 blue balls. You draw one at random. What is the probability P that it is blue?

8 / 7
P =
2.Easy
sum = 7die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 7?

2 dice= 7
P =
3.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
4.Medium
xp(x)10.120.3530.340.25μ = 2.7

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

x: 1, 2, 3, 4p(x): 0.1, 0.35, 0.3, 0.25
σ =
5.Hard
n = 5, p = 0.7: P(X ≤ 1) = ?k012345

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

n = 5p = 0.7
P =
6.Hard
€p(x)−100.8100.15900.05

A game costs €10 to play. You win €20 with probability 0.15 and €100 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€20: p = 0.15€100: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.4667
  2. 2. P = 0.1667
  3. 3. P = 0.5177
  4. 4. σ = 0.9539
  5. 5. P = 0.03078
  6. 6. E(G) = −2 €

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