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)00.3510.320.35

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
E(X) =
2.Easy
red: 8blue: 3green: 1

A bag holds 8 red, 3 blue and 1 green balls. You draw one at random. What is the probability P that it is red?

8 / 3 / 1
P =
3.Medium
P(at least one six) = ??1?2?3?4?5?6?7?8P(six) = 1/6 on each roll

A fair die is rolled 8 times. What is the probability P of getting at least one six?

n = 8
P =
4.Medium
red: 4blue: 4

A bag holds 4 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

4 / 4
P =
5.Hard
n = 10, p = 0.6: P(X ≤ 1) = ?k012345678910

10 components are tested, and each one fails with probability 0.6, independently. What is the probability P that at most one fails?

n = 10p = 0.6
P =
6.Hard
n = 7, p = 0.3: P(X = 1) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 1 correct answers?

n = 7p = 0.3k = 1
P =

Answer key

  1. 1. E(X) = 1
  2. 2. P = 0.6667
  3. 3. P = 0.7674
  4. 4. P = 0.2143
  5. 5. P = 0.001678
  6. 6. P = 0.2471

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