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)10.220.3530.1540.3

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

x: 1, 2, 3, 4p(x): 0.2, 0.35, 0.15, 0.3
E(X) =
2.Easy
xp(x)00.210.220.230.254?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 0, 1, 2, 3, 4p(x): 0.2, 0.2, 0.2, 0.25, ?
P(X = 4) =
3.Medium
red: 5blue: 3

A bag holds 5 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 3
P =
4.Medium
red: 8blue: 5

A bag holds 8 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 5
P =
5.Hard
n = 8, p = 0.1: P(X ≤ 1) = ?k012345678

8 components are tested, and each one fails with probability 0.1, independently. What is the probability P that at most one fails?

n = 8p = 0.1
P =
6.Hard
n = 11, p = 0.3: P(X ≤ 1) = ?k01234567891011

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

n = 11p = 0.3
P =

Answer key

  1. 1. E(X) = 2.55
  2. 2. P(X = 4) = 0.15
  3. 3. P = 0.3571
  4. 4. P = 0.359
  5. 5. P = 0.8131
  6. 6. P = 0.113

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