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)100.3200.3300.3400.1

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

x: 10, 20, 30, 40p(x): 0.3, 0.3, 0.3, 0.1
E(X) =
2.Easy
sum = 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 10?

2 dice= 10
P =
3.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
4.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 =
5.Hard
n = 7, p = 0.1: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.1, independently. What is the probability P that at most one fails?

n = 7p = 0.1
P =
6.Hard
n = 12, p = 0.2: P(X = 5) = ?k0123456789101112

A test has 12 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 = 12p = 0.2k = 5
P =

Answer key

  1. 1. E(X) = 22
  2. 2. P = 0.08333
  3. 3. P = 0.5177
  4. 4. σ = 0.8047
  5. 5. P = 0.8503
  6. 6. P = 0.05315

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