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)00.1510.32?30.25

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

x: 0, 1, 2, 3p(x): 0.15, 0.3, ?, 0.25
P(X = 2) =
2.Easy
xp(x)00.110.3520.0530.2540.25

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

x: 0, 1, 2, 3, 4p(x): 0.1, 0.35, 0.05, 0.25, 0.25
E(X) =
3.Medium
n = 12k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 12? The order does not matter.

n = 12k = 2
N =
4.Medium
red: 5blue: 8

A bag holds 5 red and 8 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 8
P =
5.Hard
€p(x)−10.6820.3190.02

A game costs €1 to play. You win €3 with probability 0.3 and €20 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€3: p = 0.3€20: p = 0.02
E(G) = €
6.Hard
n = 6, p = 0.1: P(X = 4) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 4 correct answers?

n = 6p = 0.1k = 4
P =

Answer key

  1. 1. P(X = 2) = 0.3
  2. 2. E(X) = 2.2
  3. 3. N = 66
  4. 4. P = 0.1282
  5. 5. E(G) = 0.3 €
  6. 6. P = 0.001215

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