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?20.2540.2560.15

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

x: 0, 2, 4, 6p(x): ?, 0.25, 0.25, 0.15
P(X = 0) =
2.Easy
xp(x)00.110.220.3530.35

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

x: 0, 1, 2, 3p(x): 0.1, 0.2, 0.35, 0.35
E(X) =
3.Medium
xp(x)10.2520.130.0540.2550.35μ = 3.35

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

x: 1, 2, 3, 4, 5p(x): 0.25, 0.1, 0.05, 0.25, 0.35
σ =
4.Medium
n = 6k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 6? The order does not matter.

n = 6k = 4
N =
5.Hard
n = 10, p = 0.7: P(X ≤ 1) = ?k012345678910

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

n = 10p = 0.7
P =
6.Hard
€p(x)−100.8300.151900.05

A game costs €10 to play. You win €40 with probability 0.15 and €200 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€40: p = 0.15€200: p = 0.05
E(G) = €

Answer key

  1. 1. P(X = 0) = 0.35
  2. 2. E(X) = 1.95
  3. 3. σ = 1.621
  4. 4. N = 15
  5. 5. P = 0.0001437
  6. 6. E(G) = 6 €

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