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: 8blue: 8green: 2

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

8 / 8 / 2
P =
2.Easy
xp(x)00.110.32?30.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 1, 2, 3p(x): 0.1, 0.3, ?, 0.25
P(X = 2) =
3.Medium
xp(x)100.3200.35300.05400.3μ = 23.5

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

x: 10, 20, 30, 40p(x): 0.3, 0.35, 0.05, 0.3
Var(X) =
4.Medium
P(at least one six) = ??1?2P(six) = 1/6 on each roll

A fair die is rolled 2 times. What is the probability P of getting at least one six?

n = 2
P =
5.Hard
xp(x)00.3510.320.35μ

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 10X + 10
σY =
6.Hard
xp(x)00.3510.3520.3μ

X has the distribution shown, and Y = 3X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.35, 0.3Y = 3X + 4
σY =

Answer key

  1. 1. P = 0.4444
  2. 2. P(X = 2) = 0.35
  3. 3. Var(X) = 142.8
  4. 4. P = 0.3056
  5. 5. σY = 8.367
  6. 6. σY = 2.414

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