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 at least 9?

2 dice≥ 9
P =
2.Easy
sum ≥ 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 3?

2 dice≥ 3
P =
3.Medium
xp(x)00.310.3520.35μ = 1.05

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
Var(X) =
4.Medium
n = 15k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 15? The order does not matter.

n = 15k = 2
N =
5.Hard
xp(x)10.0520.3530.3540.150.15μ

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

x: 1, 2, 3, 4, 5p(x): 0.05, 0.35, 0.35, 0.1, 0.15Y = −2X + 4
σY =
6.Hard
xp(x)00.0510.320.0530.340.3μ

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

x: 0, 1, 2, 3, 4p(x): 0.05, 0.3, 0.05, 0.3, 0.3Y = −2X + 10
σY =

Answer key

  1. 1. P = 0.2778
  2. 2. P = 0.9722
  3. 3. Var(X) = 0.6475
  4. 4. N = 105
  5. 5. σY = 2.234
  6. 6. σY = 2.646

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