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
xp(x)10?200.3300.3400.05

The table gives the probability distribution of X, but one probability is missing. Find P(X = 10).

x: 10, 20, 30, 40p(x): ?, 0.3, 0.3, 0.05
P(X = 10) =
2.Easy
xp(x)00.110.320.0530.340.25

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

x: 0, 1, 2, 3, 4p(x): 0.1, 0.3, 0.05, 0.3, 0.25
E(X) =
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 = 9k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 9? The order does not matter.

n = 9k = 3
N =
5.Hard
n = 10, p = 0.1: P(X ≤ 1) = ?k012345678910

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

n = 10p = 0.1
P =
6.Hard
xp(x)00.3510.120.3530.2μ

X has the distribution shown, and Y = 5X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.35, 0.1, 0.35, 0.2Y = 5X + 1
σY =

Answer key

  1. 1. P(X = 10) = 0.35
  2. 2. E(X) = 2.3
  3. 3. Var(X) = 0.6475
  4. 4. N = 84
  5. 5. P = 0.7361
  6. 6. σY = 5.788

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