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)00.3510.120.3530.2

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

x: 0, 1, 2, 3p(x): 0.35, 0.1, 0.35, 0.2
E(X) =
2.Easy
red: 2blue: 2

A bag holds 2 red and 2 blue balls. You draw one at random. What is the probability P that it is blue?

2 / 2
P =
3.Medium
xp(x)10.220.230.340.3μ = 2.7

For the distribution shown, find the variance Var(X) of X.

x: 1, 2, 3, 4p(x): 0.2, 0.2, 0.3, 0.3
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7?8P(six) = 1/6 on each roll

A fair die is rolled 8 times. What is the probability P of getting at least one six?

n = 8
P =
5.Hard
n = 11, p = 0.4: P(X ≤ 1) = ?k01234567891011

11 components are tested, and each one fails with probability 0.4, independently. What is the probability P that at most one fails?

n = 11p = 0.4
P =
6.Hard
n = 7, p = 0.6: P(X = 2) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 2 correct answers?

n = 7p = 0.6k = 2
P =

Answer key

  1. 1. E(X) = 1.4
  2. 2. P = 0.5
  3. 3. Var(X) = 1.21
  4. 4. P = 0.7674
  5. 5. P = 0.03023
  6. 6. P = 0.07741

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