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: 4blue: 4green: 4

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

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

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

8 / 2
P =
3.Medium
xp(x)00.210.0520.3530.2540.15μ = 2.1

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

x: 0, 1, 2, 3, 4p(x): 0.2, 0.05, 0.35, 0.25, 0.15
σ =
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)100.2200.2300.35400.25μ

X has the distribution shown, and Y = 0.5X + 5. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.2, 0.2, 0.35, 0.25Y = 0.5X + 5
σY =
6.Hard
xp(x)00.1510.1520.3530.35μ

X has the distribution shown, and Y = 0.5X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.15, 0.15, 0.35, 0.35Y = 0.5X + 10
σY =

Answer key

  1. 1. P = 0.6667
  2. 2. P = 0.8
  3. 3. σ = 1.3
  4. 4. P = 0.5177
  5. 5. σY = 5.309
  6. 6. σY = 0.522

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