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)00.351?20.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2p(x): 0.35, ?, 0.3
P(X = 1) =
2.Easy
xp(x)10.2520.230.0540.3550.15

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

x: 1, 2, 3, 4, 5p(x): 0.25, 0.2, 0.05, 0.35, 0.15
E(X) =
3.Medium
P(at least one six) = ??1?2?3?4?5P(six) = 1/6 on each roll

A fair die is rolled 5 times. What is the probability P of getting at least one six?

n = 5
P =
4.Medium
xp(x)10.3520.3530.0540.25μ = 2.2

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

x: 1, 2, 3, 4p(x): 0.35, 0.35, 0.05, 0.25
Var(X) =
5.Hard
n = 11, p = 0.25: P(X ≤ 1) = ?k01234567891011

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

n = 11p = 0.25
P =
6.Hard
€p(x)−50.69150.3950.01

A game costs €5 to play. You win €20 with probability 0.3 and €100 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€20: p = 0.3€100: p = 0.01
E(G) = €

Answer key

  1. 1. P(X = 1) = 0.35
  2. 2. E(X) = 2.95
  3. 3. P = 0.5981
  4. 4. Var(X) = 1.36
  5. 5. P = 0.1971
  6. 6. E(G) = 2 €

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