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)00.310.220.230.3

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

x: 0, 1, 2, 3p(x): 0.3, 0.2, 0.2, 0.3
E(X) =
2.Easy
red: 7blue: 5green: 1

A bag holds 7 red, 5 blue and 1 green balls. You draw one at random. What is the probability P that it is blue?

7 / 5 / 1
P =
3.Medium
n = 11k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 11? The order does not matter.

n = 11k = 5
N =
4.Medium
n = 13k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 13? The order does not matter.

n = 13k = 2
N =
5.Hard
€p(x)−10.810.15190.05

A game costs €1 to play. You win €2 with probability 0.15 and €20 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€2: p = 0.15€20: p = 0.05
E(G) = €
6.Hard
n = 9, p = 0.2: P(X = 2) = ?k0123456789

A test has 9 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 = 9p = 0.2k = 2
P =

Answer key

  1. 1. E(X) = 1.5
  2. 2. P = 0.3846
  3. 3. N = 462
  4. 4. N = 78
  5. 5. E(G) = 0.3 €
  6. 6. P = 0.302

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