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)00.3510.3520.3

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
E(X) =
2.Easy
sum ≥ 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 11?

2 dice≥ 11
P =
3.Medium
xp(x)00.210.0520.3530.1540.25μ = 2.2

For the distribution shown, find the variance Var(X) of X.

x: 0, 1, 2, 3, 4p(x): 0.2, 0.05, 0.35, 0.15, 0.25
Var(X) =
4.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 =
5.Hard
n = 12, p = 0.2: P(X ≤ 1) = ?k0123456789101112

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

n = 12p = 0.2
P =
6.Hard
n = 8, p = 0.1: P(X = 4) = ?k012345678

A test has 8 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 = 8p = 0.1k = 4
P =

Answer key

  1. 1. E(X) = 0.95
  2. 2. P = 0.08333
  3. 3. Var(X) = 1.96
  4. 4. P = 0.6651
  5. 5. P = 0.2749
  6. 6. P = 0.004593

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