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)00.210.3520.230.140.15

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

x: 0, 1, 2, 3, 4p(x): 0.2, 0.35, 0.2, 0.1, 0.15
E(X) =
2.Easy
red: 2blue: 3green: 3

A bag holds 2 red, 3 blue and 3 green balls. You draw one at random. What is the probability P that it is red?

2 / 3 / 3
P =
3.Medium
xp(x)00.310.320.330.1μ = 1.2

For the distribution shown, find the standard deviation σ of X.

x: 0, 1, 2, 3p(x): 0.3, 0.3, 0.3, 0.1
σ =
4.Medium
red: 8blue: 3

A bag holds 8 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 3
P =
5.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 =
6.Hard
n = 9, p = 0.5: P(X = 4) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 4 correct answers?

n = 9p = 0.5k = 4
P =

Answer key

  1. 1. E(X) = 1.65
  2. 2. P = 0.25
  3. 3. σ = 0.9798
  4. 4. P = 0.5091
  5. 5. P = 0.337
  6. 6. P = 0.2461

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