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 = 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 11?

2 dice= 11
P =
2.Easy
xp(x)00.2510.3520.2530.15

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

x: 0, 1, 2, 3p(x): 0.25, 0.35, 0.25, 0.15
E(X) =
3.Medium
n = 10k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 10? The order does not matter.

n = 10k = 4
N =
4.Medium
xp(x)00.210.0520.230.3540.2μ = 2.3

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

x: 0, 1, 2, 3, 4p(x): 0.2, 0.05, 0.2, 0.35, 0.2
Var(X) =
5.Hard
xp(x)10.320.2530.140.35μ

X has the distribution shown, and Y = 3X + 10. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.3, 0.25, 0.1, 0.35Y = 3X + 10
σY =
6.Hard
n = 7, p = 0.4: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.4, independently. What is the probability P that at most one fails?

n = 7p = 0.4
P =

Answer key

  1. 1. P = 0.05556
  2. 2. E(X) = 1.3
  3. 3. N = 210
  4. 4. Var(X) = 1.91
  5. 5. σY = 3.735
  6. 6. P = 0.1586

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