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)00.1520.3540.3560.15

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

x: 0, 2, 4, 6p(x): 0.15, 0.35, 0.35, 0.15
E(X) =
2.Easy
red: 7blue: 2green: 2

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

7 / 2 / 2
P =
3.Medium
n = 12k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 12? The order does not matter.

n = 12k = 3
N =
4.Medium
n = 8k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 8? The order does not matter.

n = 8k = 3
N =
5.Hard
€p(x)−100.75400.2900.05

A game costs €10 to play. You win €50 with probability 0.2 and €100 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€50: p = 0.2€100: p = 0.05
E(G) = €
6.Hard
n = 9, p = 0.7: P(X = 4) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 4 correct answers?

n = 9p = 0.7k = 4
P =

Answer key

  1. 1. E(X) = 3
  2. 2. P = 0.3636
  3. 3. N = 220
  4. 4. N = 56
  5. 5. E(G) = 5 €
  6. 6. P = 0.07351

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