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)0?10.3520.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 1, 2p(x): ?, 0.35, 0.3
P(X = 0) =
2.Easy
red: 4blue: 2green: 1

A bag holds 4 red, 2 blue and 1 green balls. You draw one at random. What is the probability P that it is not red?

4 / 2 / 1
P =
3.Medium
xp(x)00.220.3540.3560.1μ = 2.7

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

x: 0, 2, 4, 6p(x): 0.2, 0.35, 0.35, 0.1
Var(X) =
4.Medium
n = 13k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 13? The order does not matter.

n = 13k = 5
N =
5.Hard
n = 7, p = 0.1: P(X ≤ 1) = ?k01234567

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

n = 7p = 0.1
P =
6.Hard
n = 11, p = 0.7: P(X = 2) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 2 correct answers?

n = 11p = 0.7k = 2
P =

Answer key

  1. 1. P(X = 0) = 0.35
  2. 2. P = 0.4286
  3. 3. Var(X) = 3.31
  4. 4. N = 1287
  5. 5. P = 0.8503
  6. 6. P = 0.0005305

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