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 = 6die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 6?

2 dice= 6
P =
2.Easy
xp(x)100.25200.3300.15400.3

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

x: 10, 20, 30, 40p(x): 0.25, 0.3, 0.15, 0.3
E(X) =
3.Medium
n = 9k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 9? The order does not matter.

n = 9k = 4
N =
4.Medium
n = 10k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 10? The order does not matter.

n = 10k = 2
N =
5.Hard
n = 10, p = 0.5: P(X = 2) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 2 correct answers?

n = 10p = 0.5k = 2
P =
6.Hard
n = 10, p = 0.1: P(X = 4) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 4 correct answers?

n = 10p = 0.1k = 4
P =

Answer key

  1. 1. P = 0.1389
  2. 2. E(X) = 25
  3. 3. N = 126
  4. 4. N = 45
  5. 5. P = 0.04395
  6. 6. P = 0.01116

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