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)00.210.22?30.35

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

x: 0, 1, 2, 3p(x): 0.2, 0.2, ?, 0.35
P(X = 2) =
2.Easy
red: 8blue: 8green: 1

A bag holds 8 red, 8 blue and 1 green balls. You draw one at random. What is the probability P that it is blue?

8 / 8 / 1
P =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
4.Medium
red: 7blue: 8

A bag holds 7 red and 8 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 8
P =
5.Hard
€p(x)−10.7930.290.01

A game costs €1 to play. You win €4 with probability 0.2 and €10 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€4: p = 0.2€10: p = 0.01
E(G) = €
6.Hard
n = 12, p = 0.25: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 12p = 0.25
P =

Answer key

  1. 1. P(X = 2) = 0.25
  2. 2. P = 0.4706
  3. 3. Var(X) = 0.6475
  4. 4. P = 0.2
  5. 5. E(G) = −0.1 €
  6. 6. P = 0.1584

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