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)100.25200.2300.35400.2

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

x: 10, 20, 30, 40p(x): 0.25, 0.2, 0.35, 0.2
E(X) =
2.Easy
xp(x)00.210.3520.253?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 0, 1, 2, 3p(x): 0.2, 0.35, 0.25, ?
P(X = 3) =
3.Medium
xp(x)00.2510.2520.130.1540.25μ = 1.9

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

x: 0, 1, 2, 3, 4p(x): 0.25, 0.25, 0.1, 0.15, 0.25
σ =
4.Medium
xp(x)00.1510.2520.2530.35μ = 1.8

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

x: 0, 1, 2, 3p(x): 0.15, 0.25, 0.25, 0.35
Var(X) =
5.Hard
n = 9, p = 0.25: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 9p = 0.25
P =
6.Hard
n = 12, p = 0.1: P(X = 2) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 2 correct answers?

n = 12p = 0.1k = 2
P =

Answer key

  1. 1. E(X) = 25
  2. 2. P(X = 3) = 0.2
  3. 3. σ = 1.546
  4. 4. Var(X) = 1.16
  5. 5. P = 0.3003
  6. 6. P = 0.2301

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