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 ≥ 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 5?

2 dice≥ 5
P =
2.Easy
xp(x)00.120.3540.2560.3

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

x: 0, 2, 4, 6p(x): 0.1, 0.35, 0.25, 0.3
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
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
σ =
5.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 =
6.Hard
xp(x)00.1520.3540.2560.25μ

X has the distribution shown, and Y = −2X + 20. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.15, 0.35, 0.25, 0.25Y = −2X + 20
σY =

Answer key

  1. 1. P = 0.8333
  2. 2. E(X) = 3.5
  3. 3. P = 0.2333
  4. 4. σ = 0.8047
  5. 5. P = 0.1971
  6. 6. σY = 4.079

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