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.

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1.Easy
xp(x)00.3510.320.35

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
E(X) =
2.Easy
xp(x)10.252?30.340.3

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

x: 1, 2, 3, 4p(x): 0.25, ?, 0.3, 0.3
P(X = 2) =
3.Medium
red: 5blue: 3

A bag holds 5 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 3
P =
4.Medium
red: 4blue: 9

A bag holds 4 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

4 / 9
P =
5.Hard
€p(x)−20.7920.2180.01

A game costs €2 to play. You win €4 with probability 0.2 and €20 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€4: p = 0.2€20: p = 0.01
E(G) = €
6.Hard
n = 6, p = 0.1: P(X = 2) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 2 correct answers?

n = 6p = 0.1k = 2
P =

Answer key

  1. 1. E(X) = 1
  2. 2. P(X = 2) = 0.15
  3. 3. P = 0.3571
  4. 4. P = 0.07692
  5. 5. E(G) = −1 €
  6. 6. P = 0.09842

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