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)00.2510.2520.330.2

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

x: 0, 1, 2, 3p(x): 0.25, 0.25, 0.3, 0.2
E(X) =
2.Easy
sum = 7die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 7?

2 dice= 7
P =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

For the distribution shown, find the standard deviation σ of X.

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
σ =
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 = 11, p = 0.2: P(X ≤ 1) = ?k01234567891011

11 components are tested, and each one fails with probability 0.2, independently. What is the probability P that at most one fails?

n = 11p = 0.2
P =
6.Hard
n = 12, p = 0.5: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.5, independently. What is the probability P that at most one fails?

n = 12p = 0.5
P =

Answer key

  1. 1. E(X) = 1.45
  2. 2. P = 0.1667
  3. 3. σ = 0.8047
  4. 4. P = 0.7674
  5. 5. P = 0.3221
  6. 6. P = 0.003174

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