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 = 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 10?

2 dice= 10
P =
2.Easy
xp(x)00.110.220.2530.240.25

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 0, 1, 2, 3, 4p(x): 0.1, 0.2, 0.25, 0.2, 0.25
E(X) =
3.Medium
xp(x)00.0510.320.3530.3μ = 1.9

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

x: 0, 1, 2, 3p(x): 0.05, 0.3, 0.35, 0.3
Var(X) =
4.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 =
5.Hard
n = 11, p = 0.3: P(X ≤ 1) = ?k01234567891011

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

n = 11p = 0.3
P =
6.Hard
xp(x)10.320.3530.140.250.05μ

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.35, 0.1, 0.2, 0.05Y = 10X + 20
σY =

Answer key

  1. 1. P = 0.08333
  2. 2. E(X) = 2.3
  3. 3. Var(X) = 0.79
  4. 4. N = 1001
  5. 5. P = 0.113
  6. 6. σY = 12.36

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