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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Name: ____________________   Date: ____________

1.Easy
red: 5blue: 6green: 4

A bag holds 5 red, 6 blue and 4 green balls. You draw one at random. What is the probability P that it is red?

5 / 6 / 4
P =
2.Easy
sum = 8die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 8?

2 dice= 8
P =
3.Medium
red: 8blue: 9

A bag holds 8 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 9
P =
4.Medium
xp(x)100.3200.15300.25400.3μ = 25.5

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

x: 10, 20, 30, 40p(x): 0.3, 0.15, 0.25, 0.3
Var(X) =
5.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 =
6.Hard
n = 9, p = 0.25: P(X = 5) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 5 correct answers?

n = 9p = 0.25k = 5
P =

Answer key

  1. 1. P = 0.3333
  2. 2. P = 0.1389
  3. 3. P = 0.2059
  4. 4. Var(X) = 144.8
  5. 5. P = 0.001678
  6. 6. P = 0.03893

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