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)10.3520.230.140.155?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 5).

x: 1, 2, 3, 4, 5p(x): 0.35, 0.2, 0.1, 0.15, ?
P(X = 5) =
2.Easy
xp(x)10.120.2530.340.35

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

x: 1, 2, 3, 4p(x): 0.1, 0.25, 0.3, 0.35
E(X) =
3.Medium
red: 3blue: 4

A bag holds 3 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 4
P =
4.Medium
red: 6blue: 8

A bag holds 6 red and 8 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 8
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 = 8, p = 0.25: P(X ≤ 1) = ?k012345678

8 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 8p = 0.25
P =

Answer key

  1. 1. P(X = 5) = 0.2
  2. 2. E(X) = 2.9
  3. 3. P = 0.1429
  4. 4. P = 0.1648
  5. 5. P = 0.8131
  6. 6. P = 0.3671

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