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)00.310.1520.230.35

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

x: 0, 1, 2, 3p(x): 0.3, 0.15, 0.2, 0.35
E(X) =
2.Easy
red: 6blue: 7green: 2

A bag holds 6 red, 7 blue and 2 green balls. You draw one at random. What is the probability P that it is not red?

6 / 7 / 2
P =
3.Medium
red: 8blue: 3

A bag holds 8 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 3
P =
4.Medium
red: 8blue: 4

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

8 / 4
P =
5.Hard
€p(x)−50.73200.25950.02

A game costs €5 to play. You win €25 with probability 0.25 and €100 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€25: p = 0.25€100: p = 0.02
E(G) = €
6.Hard
n = 7, p = 0.1: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.1, independently. What is the probability P that at most one fails?

n = 7p = 0.1
P =

Answer key

  1. 1. E(X) = 1.6
  2. 2. P = 0.6
  3. 3. P = 0.5091
  4. 4. P = 0.4242
  5. 5. E(G) = 3.25 €
  6. 6. P = 0.8503

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