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
sum ≥ 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 4?

2 dice≥ 4
P =
2.Easy
xp(x)100.3200.35300.2400.15

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

x: 10, 20, 30, 40p(x): 0.3, 0.35, 0.2, 0.15
E(X) =
3.Medium
red: 8blue: 8

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

8 / 8
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 = 5, p = 0.1: P(X ≤ 1) = ?k012345

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

n = 5p = 0.1
P =
6.Hard
n = 11, p = 0.25: P(X ≤ 1) = ?k01234567891011

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

n = 11p = 0.25
P =

Answer key

  1. 1. P = 0.9167
  2. 2. E(X) = 22
  3. 3. P = 0.2333
  4. 4. P = 0.1648
  5. 5. P = 0.9185
  6. 6. P = 0.1971

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