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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1.Easy
xp(x)0?20.140.3560.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 2, 4, 6p(x): ?, 0.1, 0.35, 0.25
P(X = 0) =
2.Easy
xp(x)10?200.35300.25400.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 10).

x: 10, 20, 30, 40p(x): ?, 0.35, 0.25, 0.35
P(X = 10) =
3.Medium
red: 7blue: 4

A bag holds 7 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 4
P =
4.Medium
xp(x)100.2200.25300.35400.2μ = 25.5

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

x: 10, 20, 30, 40p(x): 0.2, 0.25, 0.35, 0.2
σ =
5.Hard
xp(x)10.120.2530.240.150.35μ

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

x: 1, 2, 3, 4, 5p(x): 0.1, 0.25, 0.2, 0.1, 0.35Y = 10X + 4
σY =
6.Hard
xp(x)00.2510.120.0530.3540.25μ

X has the distribution shown, and Y = 3X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.25, 0.1, 0.05, 0.35, 0.25Y = 3X + 1
σY =

Answer key

  1. 1. P(X = 0) = 0.3
  2. 2. P(X = 10) = 0.05
  3. 3. P = 0.3818
  4. 4. σ = 10.23
  5. 5. σY = 14.24
  6. 6. σY = 4.635

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