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)10.152?30.240.2550.35

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

x: 1, 2, 3, 4, 5p(x): 0.15, ?, 0.2, 0.25, 0.35
P(X = 2) =
2.Easy
xp(x)00.1520.3540.360.2

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, 0.3, 0.2
E(X) =
3.Medium
xp(x)00.2510.220.330.25μ = 1.55

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

x: 0, 1, 2, 3p(x): 0.25, 0.2, 0.3, 0.25
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5?6P(six) = 1/6 on each roll

A fair die is rolled 6 times. What is the probability P of getting at least one six?

n = 6
P =
5.Hard
n = 11, p = 0.7: P(X ≤ 1) = ?k01234567891011

11 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 11p = 0.7
P =
6.Hard
€p(x)−20.8560.1380.05

A game costs €2 to play. You win €8 with probability 0.1 and €40 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€8: p = 0.1€40: p = 0.05
E(G) = €

Answer key

  1. 1. P(X = 2) = 0.05
  2. 2. E(X) = 3.1
  3. 3. Var(X) = 1.247
  4. 4. P = 0.6651
  5. 5. P = 4.724 × 10⁻⁵
  6. 6. E(G) = 0.8 €

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