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
sum ≥ 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 9?

2 dice≥ 9
P =
2.Easy
red: 5blue: 3green: 4

A bag holds 5 red, 3 blue and 4 green balls. You draw one at random. What is the probability P that it is red?

5 / 3 / 4
P =
3.Medium
P(at least one six) = ??1?2?3P(six) = 1/6 on each roll

A fair die is rolled 3 times. What is the probability P of getting at least one six?

n = 3
P =
4.Medium
xp(x)00.210.120.0530.340.35μ = 2.5

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

x: 0, 1, 2, 3, 4p(x): 0.2, 0.1, 0.05, 0.3, 0.35
Var(X) =
5.Hard
n = 10, p = 0.3: P(X ≤ 1) = ?k012345678910

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

n = 10p = 0.3
P =
6.Hard
n = 7, p = 0.1: P(X = 3) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 3 correct answers?

n = 7p = 0.1k = 3
P =

Answer key

  1. 1. P = 0.2778
  2. 2. P = 0.4167
  3. 3. P = 0.4213
  4. 4. Var(X) = 2.35
  5. 5. P = 0.1493
  6. 6. P = 0.02296

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