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)100.3200.35300.25400.1

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

x: 10, 20, 30, 40p(x): 0.3, 0.35, 0.25, 0.1
E(X) =
2.Easy
sum = 7die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 7?

2 dice= 7
P =
3.Medium
xp(x)00.210.0520.330.240.25μ = 2.25

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

x: 0, 1, 2, 3, 4p(x): 0.2, 0.05, 0.3, 0.2, 0.25
Var(X) =
4.Medium
red: 6blue: 9

A bag holds 6 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 9
P =
5.Hard
n = 9, p = 0.3: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.3, independently. What is the probability P that at most one fails?

n = 9p = 0.3
P =
6.Hard
n = 10, p = 0.6: P(X ≤ 1) = ?k012345678910

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

n = 10p = 0.6
P =

Answer key

  1. 1. E(X) = 21.5
  2. 2. P = 0.1667
  3. 3. Var(X) = 1.987
  4. 4. P = 0.1429
  5. 5. P = 0.196
  6. 6. P = 0.001678

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