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)00.210.220.2530.35

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

x: 0, 1, 2, 3p(x): 0.2, 0.2, 0.25, 0.35
E(X) =
2.Easy
red: 2blue: 6green: 1

A bag holds 2 red, 6 blue and 1 green balls. You draw one at random. What is the probability P that it is blue?

2 / 6 / 1
P =
3.Medium
xp(x)100.35200.15300.15400.35μ = 25

For the distribution shown, find the standard deviation σ of X.

x: 10, 20, 30, 40p(x): 0.35, 0.15, 0.15, 0.35
σ =
4.Medium
red: 8blue: 9

A bag holds 8 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 9
P =
5.Hard
€p(x)−10.8440.1590.01

A game costs €1 to play. You win €5 with probability 0.15 and €10 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€5: p = 0.15€10: p = 0.01
E(G) = €
6.Hard
n = 8, p = 0.25: P(X ≤ 1) = ?k012345678

8 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 8p = 0.25
P =

Answer key

  1. 1. E(X) = 1.75
  2. 2. P = 0.6667
  3. 3. σ = 12.85
  4. 4. P = 0.2059
  5. 5. E(G) = −0.15 €
  6. 6. P = 0.3671

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