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: 7green: 4

A bag holds 7 red, 7 blue and 4 green balls. You draw one at random. What is the probability P that it is not red?

7 / 7 / 4
P =
2.Easy
red: 2blue: 5green: 2

A bag holds 2 red, 5 blue and 2 green balls. You draw one at random. What is the probability P that it is not red?

2 / 5 / 2
P =
3.Medium
xp(x)00.310.320.1530.25μ = 1.35

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

x: 0, 1, 2, 3p(x): 0.3, 0.3, 0.15, 0.25
σ =
4.Medium
xp(x)00.2510.1520.230.240.2μ = 1.95

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

x: 0, 1, 2, 3, 4p(x): 0.25, 0.15, 0.2, 0.2, 0.2
Var(X) =
5.Hard
n = 6, p = 0.3: P(X = 2) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 2 correct answers?

n = 6p = 0.3k = 2
P =
6.Hard
€p(x)−10.8810.1490.02

A game costs €1 to play. You win €2 with probability 0.1 and €50 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€2: p = 0.1€50: p = 0.02
E(G) = €

Answer key

  1. 1. P = 0.6111
  2. 2. P = 0.7778
  3. 3. σ = 1.152
  4. 4. Var(X) = 2.147
  5. 5. P = 0.3241
  6. 6. E(G) = 0.2 €

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