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: 7green: 5

A bag holds 5 red, 7 blue and 5 green balls. You draw one at random. What is the probability P that it is red?

5 / 7 / 5
P =
2.Easy
red: 7blue: 7green: 3

A bag holds 7 red, 7 blue and 3 green balls. You draw one at random. What is the probability P that it is not red?

7 / 7 / 3
P =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
4.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 =
5.Hard
xp(x)00.3520.340.0560.3μ

X has the distribution shown, and Y = 10X + 4. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.35, 0.3, 0.05, 0.3Y = 10X + 4
σY =
6.Hard
xp(x)00.3510.220.1530.3μ

X has the distribution shown, and Y = 2X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.35, 0.2, 0.15, 0.3Y = 2X + 10
σY =

Answer key

  1. 1. P = 0.2941
  2. 2. P = 0.5882
  3. 3. Var(X) = 0.6475
  4. 4. P = 0.5177
  5. 5. σY = 24.58
  6. 6. σY = 2.482

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