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)10.220.330.14?50.25

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.3, 0.1, ?, 0.25
P(X = 4) =
2.Easy
red: 8blue: 3green: 3

A bag holds 8 red, 3 blue and 3 green balls. You draw one at random. What is the probability P that it is not red?

8 / 3 / 3
P =
3.Medium
xp(x)00.3510.320.35μ = 1

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

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

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

4 / 4
P =
5.Hard
n = 12, p = 0.6: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.6, independently. What is the probability P that at most one fails?

n = 12p = 0.6
P =
6.Hard
€p(x)−30.8930.11470.01

A game costs €3 to play. You win €6 with probability 0.1 and €150 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€6: p = 0.1€150: p = 0.01
E(G) = €

Answer key

  1. 1. P(X = 4) = 0.15
  2. 2. P = 0.4286
  3. 3. Var(X) = 0.7
  4. 4. P = 0.2143
  5. 5. P = 0.0003188
  6. 6. E(G) = −0.9 €

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