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)0?20.3540.2560.2

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 2, 4, 6p(x): ?, 0.35, 0.25, 0.2
P(X = 0) =
2.Easy
xp(x)10.1520.2530.3540.0550.2

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

x: 1, 2, 3, 4, 5p(x): 0.15, 0.25, 0.35, 0.05, 0.2
E(X) =
3.Medium
red: 6blue: 6

A bag holds 6 red and 6 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 6
P =
4.Medium
xp(x)00.320.1540.2560.3μ = 3.1

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

x: 0, 2, 4, 6p(x): 0.3, 0.15, 0.25, 0.3
σ =
5.Hard
n = 11, p = 0.5: P(X ≤ 1) = ?k01234567891011

11 components are tested, and each one fails with probability 0.5, independently. What is the probability P that at most one fails?

n = 11p = 0.5
P =
6.Hard
€p(x)−10.8540.1490.05

A game costs €1 to play. You win €5 with probability 0.1 and €50 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€5: p = 0.1€50: p = 0.05
E(G) = €

Answer key

  1. 1. P(X = 0) = 0.2
  2. 2. E(X) = 2.9
  3. 3. P = 0.2273
  4. 4. σ = 2.406
  5. 5. P = 0.005859
  6. 6. E(G) = 2 €

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