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
xp(x)10.0520.130.2540.355?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 5).

x: 1, 2, 3, 4, 5p(x): 0.05, 0.1, 0.25, 0.35, ?
P(X = 5) =
3.Medium
P(at least one six) = ??1?2?3P(six) = 1/6 on each roll

A fair die is rolled 3 times. What is the probability P of getting at least one six?

n = 3
P =
4.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 =
5.Hard
n = 6, p = 0.3: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.3, independently. What is the probability P that at most one fails?

n = 6p = 0.3
P =
6.Hard
n = 7, p = 0.4: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.4, independently. What is the probability P that at most one fails?

n = 7p = 0.4
P =

Answer key

  1. 1. E(X) = 1
  2. 2. P(X = 5) = 0.25
  3. 3. P = 0.4213
  4. 4. P = 0.7674
  5. 5. P = 0.4202
  6. 6. P = 0.1586

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