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)00.210.320.1530.35

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

x: 0, 1, 2, 3p(x): 0.2, 0.3, 0.15, 0.35
E(X) =
2.Easy
xp(x)10.12?30.340.35

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

x: 1, 2, 3, 4p(x): 0.1, ?, 0.3, 0.35
P(X = 2) =
3.Medium
red: 5blue: 9

A bag holds 5 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 9
P =
4.Medium
xp(x)00.2520.1540.3560.25μ = 3.2

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

x: 0, 2, 4, 6p(x): 0.25, 0.15, 0.35, 0.25
σ =
5.Hard
€p(x)−100.7200.254900.05

A game costs €10 to play. You win €30 with probability 0.25 and €500 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€30: p = 0.25€500: p = 0.05
E(G) = €
6.Hard
n = 7, p = 0.3: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.3, independently. What is the probability P that at most one fails?

n = 7p = 0.3
P =

Answer key

  1. 1. E(X) = 1.65
  2. 2. P(X = 2) = 0.25
  3. 3. P = 0.1099
  4. 4. σ = 2.227
  5. 5. E(G) = 22.5 €
  6. 6. P = 0.3294

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