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: 7blue: 3green: 1

A bag holds 7 red, 3 blue and 1 green balls. You draw one at random. What is the probability P that it is not red?

7 / 3 / 1
P =
2.Easy
xp(x)00.220.340.1560.35

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 0, 2, 4, 6p(x): 0.2, 0.3, 0.15, 0.35
E(X) =
3.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
4.Medium
xp(x)00.3510.2520.0530.2540.1μ = 1.5

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.25, 0.05, 0.25, 0.1
Var(X) =
5.Hard
xp(x)10.3520.230.1540.250.1μ

X has the distribution shown, and Y = 2X + 20. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.35, 0.2, 0.15, 0.2, 0.1Y = 2X + 20
σY =
6.Hard
xp(x)00.210.1520.330.35μ

X has the distribution shown, and Y = 5X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.2, 0.15, 0.3, 0.35Y = 5X + 10
σY =

Answer key

  1. 1. P = 0.3636
  2. 2. E(X) = 3.3
  3. 3. P = 0.7209
  4. 4. Var(X) = 2.05
  5. 5. σY = 2.793
  6. 6. σY = 5.612

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