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)10.120.130.1540.350.35

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

x: 1, 2, 3, 4, 5p(x): 0.1, 0.1, 0.15, 0.3, 0.35
E(X) =
2.Easy
sum = 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 9?

2 dice= 9
P =
3.Medium
P(at least one six) = ??1?2?3?4?5?6P(six) = 1/6 on each roll

A fair die is rolled 6 times. What is the probability P of getting at least one six?

n = 6
P =
4.Medium
n = 15k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 15? The order does not matter.

n = 15k = 4
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
n = 6, p = 0.2: P(X = 5) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 5 correct answers?

n = 6p = 0.2k = 5
P =

Answer key

  1. 1. E(X) = 3.7
  2. 2. P = 0.1111
  3. 3. P = 0.6651
  4. 4. N = 1365
  5. 5. P = 0.7361
  6. 6. P = 0.001536

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