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 ≥ 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

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

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

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

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
4.Medium
xp(x)00.320.240.360.2μ = 2.8

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

x: 0, 2, 4, 6p(x): 0.3, 0.2, 0.3, 0.2
Var(X) =
5.Hard
n = 12, p = 0.7: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 12p = 0.7
P =
6.Hard
n = 12, p = 0.6: P(X ≤ 1) = ?k0123456789101112

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

n = 12p = 0.6
P =

Answer key

  1. 1. P = 0.9722
  2. 2. P = 0.3333
  3. 3. P = 0.5177
  4. 4. Var(X) = 4.96
  5. 5. P = 1.541 × 10⁻⁵
  6. 6. P = 0.0003188

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