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
sum = 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice= 9
P =
2.Easy
sum = 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 4?

2 dice= 4
P =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
4.Medium
n = 12k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 12? The order does not matter.

n = 12k = 5
N =
5.Hard
xp(x)00.3520.240.3560.1μ

X has the distribution shown, and Y = 10X + 20. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.35, 0.2, 0.35, 0.1Y = 10X + 20
σY =
6.Hard
n = 10, p = 0.3: P(X ≤ 1) = ?k012345678910

10 components are tested, and each one fails with probability 0.3, independently. What is the probability P that at most one fails?

n = 10p = 0.3
P =

Answer key

  1. 1. P = 0.1111
  2. 2. P = 0.08333
  3. 3. Var(X) = 0.6475
  4. 4. N = 792
  5. 5. σY = 20.59
  6. 6. P = 0.1493

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