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)00.110.120.330.1540.35

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

x: 0, 1, 2, 3, 4p(x): 0.1, 0.1, 0.3, 0.15, 0.35
E(X) =
2.Easy
red: 6blue: 5green: 3

A bag holds 6 red, 5 blue and 3 green balls. You draw one at random. What is the probability P that it is blue?

6 / 5 / 3
P =
3.Medium
xp(x)00.310.2520.230.25μ = 1.4

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

x: 0, 1, 2, 3p(x): 0.3, 0.25, 0.2, 0.25
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
5.Hard
n = 6, p = 0.1: P(X = 1) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 1 correct answers?

n = 6p = 0.1k = 1
P =
6.Hard
n = 5, p = 0.4: P(X ≤ 1) = ?k012345

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

n = 5p = 0.4
P =

Answer key

  1. 1. E(X) = 2.55
  2. 2. P = 0.3571
  3. 3. Var(X) = 1.34
  4. 4. P = 0.7209
  5. 5. P = 0.3543
  6. 6. P = 0.337

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