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
xp(x)00.310.120.3530.14?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 0, 1, 2, 3, 4p(x): 0.3, 0.1, 0.35, 0.1, ?
P(X = 4) =
2.Easy
xp(x)00.32?40.3560.1

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 2, 4, 6p(x): 0.3, ?, 0.35, 0.1
P(X = 2) =
3.Medium
xp(x)10.1520.130.140.350.35μ = 3.6

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

x: 1, 2, 3, 4, 5p(x): 0.15, 0.1, 0.1, 0.3, 0.35
σ =
4.Medium
red: 4blue: 8

A bag holds 4 red and 8 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

4 / 8
P =
5.Hard
€p(x)−100.69100.34900.01

A game costs €10 to play. You win €20 with probability 0.3 and €500 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€20: p = 0.3€500: p = 0.01
E(G) = €
6.Hard
n = 5, p = 0.2: P(X = 2) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 2 correct answers?

n = 5p = 0.2k = 2
P =

Answer key

  1. 1. P(X = 4) = 0.15
  2. 2. P(X = 2) = 0.25
  3. 3. σ = 1.428
  4. 4. P = 0.09091
  5. 5. E(G) = 1 €
  6. 6. P = 0.2048

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