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: 2blue: 7green: 3

A bag holds 2 red, 7 blue and 3 green balls. You draw one at random. What is the probability P that it is not red?

2 / 7 / 3
P =
2.Easy
xp(x)00.31?20.230.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2, 3p(x): 0.3, ?, 0.2, 0.25
P(X = 1) =
3.Medium
red: 3blue: 7

A bag holds 3 red and 7 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 7
P =
4.Medium
xp(x)100.3200.05300.35400.3μ = 26.5

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

x: 10, 20, 30, 40p(x): 0.3, 0.05, 0.35, 0.3
σ =
5.Hard
xp(x)00.3510.320.130.1540.1μ

X has the distribution shown, and Y = 5X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.35, 0.3, 0.1, 0.15, 0.1Y = 5X + 4
σY =
6.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = 2X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 2X + 4
σY =

Answer key

  1. 1. P = 0.8333
  2. 2. P(X = 1) = 0.25
  3. 3. P = 0.06667
  4. 4. σ = 11.95
  5. 5. σY = 6.759
  6. 6. σY = 1.673

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