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)100.15200.35300.15400.35

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

x: 10, 20, 30, 40p(x): 0.15, 0.35, 0.15, 0.35
E(X) =
2.Easy
sum ≥ 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 3?

2 dice≥ 3
P =
3.Medium
red: 7blue: 9

A bag holds 7 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 9
P =
4.Medium
red: 3blue: 8

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

3 / 8
P =
5.Hard
n = 10, p = 0.25: P(X ≤ 1) = ?k012345678910

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

n = 10p = 0.25
P =
6.Hard
xp(x)10.220.2530.3540.2μ

X has the distribution shown, and Y = 3X + 1. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.2, 0.25, 0.35, 0.2Y = 3X + 1
σY =

Answer key

  1. 1. E(X) = 27
  2. 2. P = 0.9722
  3. 3. P = 0.175
  4. 4. P = 0.05455
  5. 5. P = 0.244
  6. 6. σY = 3.07

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