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)00.320.240.3560.15

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

x: 0, 2, 4, 6p(x): 0.3, 0.2, 0.35, 0.15
E(X) =
2.Easy
sum ≥ 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 10?

2 dice≥ 10
P =
3.Medium
red: 7blue: 7

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

7 / 7
P =
4.Medium
xp(x)100.3200.05300.3400.35μ = 27

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

x: 10, 20, 30, 40p(x): 0.3, 0.05, 0.3, 0.35
σ =
5.Hard
xp(x)10.3520.330.2540.1μ

X has the distribution shown, and Y = 0.5X + 1. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.35, 0.3, 0.25, 0.1Y = 0.5X + 1
σY =
6.Hard
n = 6, p = 0.6: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.6, independently. What is the probability P that at most one fails?

n = 6p = 0.6
P =

Answer key

  1. 1. E(X) = 2.7
  2. 2. P = 0.1667
  3. 3. P = 0.2308
  4. 4. σ = 12.29
  5. 5. σY = 0.4975
  6. 6. P = 0.04096

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