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: 8blue: 2green: 4

A bag holds 8 red, 2 blue and 4 green balls. You draw one at random. What is the probability P that it is not red?

8 / 2 / 4
P =
2.Easy
red: 3blue: 8green: 2

A bag holds 3 red, 8 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

3 / 8 / 2
P =
3.Medium
red: 8blue: 3

A bag holds 8 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 3
P =
4.Medium
xp(x)00.2520.1540.3560.25μ = 3.2

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

x: 0, 2, 4, 6p(x): 0.25, 0.15, 0.35, 0.25
σ =
5.Hard
n = 7, p = 0.1: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.1, independently. What is the probability P that at most one fails?

n = 7p = 0.1
P =
6.Hard
xp(x)00.2510.1520.330.3μ

X has the distribution shown, and Y = 0.5X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.25, 0.15, 0.3, 0.3Y = 0.5X + 4
σY =

Answer key

  1. 1. P = 0.4286
  2. 2. P = 0.2308
  3. 3. P = 0.5091
  4. 4. σ = 2.227
  5. 5. P = 0.8503
  6. 6. σY = 0.5761

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