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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Name: ____________________   Date: ____________

1.Easy
red: 4blue: 5green: 1

A bag holds 4 red, 5 blue and 1 green balls. You draw one at random. What is the probability P that it is red?

4 / 5 / 1
P =
2.Easy
xp(x)10.3520.2530.1540.250.05

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

x: 1, 2, 3, 4, 5p(x): 0.35, 0.25, 0.15, 0.2, 0.05
E(X) =
3.Medium
xp(x)00.3510.220.0530.140.3μ = 1.8

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.2, 0.05, 0.1, 0.3
Var(X) =
4.Medium
n = 11k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 11? The order does not matter.

n = 11k = 3
N =
5.Hard
€p(x)−30.8460.15570.01

A game costs €3 to play. You win €9 with probability 0.15 and €60 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€9: p = 0.15€60: p = 0.01
E(G) = €
6.Hard
n = 11, p = 0.6: P(X ≤ 1) = ?k01234567891011

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

n = 11p = 0.6
P =

Answer key

  1. 1. P = 0.4
  2. 2. E(X) = 2.35
  3. 3. Var(X) = 2.86
  4. 4. N = 165
  5. 5. E(G) = −1.05 €
  6. 6. P = 0.000734

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