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)00.310.3520.35

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
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
n = 13k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 13? The order does not matter.

n = 13k = 3
N =
4.Medium
xp(x)100.35200.25300.25400.15μ = 22

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

x: 10, 20, 30, 40p(x): 0.35, 0.25, 0.25, 0.15
Var(X) =
5.Hard
n = 10, p = 0.4: P(X ≤ 1) = ?k012345678910

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

n = 10p = 0.4
P =
6.Hard
n = 9, p = 0.25: P(X = 1) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 1 correct answers?

n = 9p = 0.25k = 1
P =

Answer key

  1. 1. E(X) = 1.05
  2. 2. P = 0.08333
  3. 3. N = 286
  4. 4. Var(X) = 116
  5. 5. P = 0.04636
  6. 6. P = 0.2253

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