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: 7green: 2

A bag holds 7 red, 7 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

7 / 7 / 2
P =
2.Easy
sum = 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 9?

2 dice= 9
P =
3.Medium
n = 14k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 14? The order does not matter.

n = 14k = 4
N =
4.Medium
xp(x)10.320.230.140.0550.35μ = 2.95

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.2, 0.1, 0.05, 0.35
σ =
5.Hard
n = 11, p = 0.1: P(X ≤ 1) = ?k01234567891011

11 components are tested, and each one fails with probability 0.1, independently. What is the probability P that at most one fails?

n = 11p = 0.1
P =
6.Hard
xp(x)00.3510.3520.3μ

X has the distribution shown, and Y = 2X + 10. Find the standard deviation σY of Y.

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

Answer key

  1. 1. P = 0.4375
  2. 2. P = 0.1111
  3. 3. N = 1001
  4. 4. σ = 1.687
  5. 5. P = 0.6974
  6. 6. σY = 1.609

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