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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Name: ____________________   Date: ____________

1.Easy
sum = 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice= 11
P =
2.Easy
xp(x)10.120.0530.2540.3550.25

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

x: 1, 2, 3, 4, 5p(x): 0.1, 0.05, 0.25, 0.35, 0.25
E(X) =
3.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
σ =
4.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
5.Hard
n = 8, p = 0.4: P(X = 3) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 3 correct answers?

n = 8p = 0.4k = 3
P =
6.Hard
€p(x)−100.84400.15900.01

A game costs €10 to play. You win €50 with probability 0.15 and €100 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€50: p = 0.15€100: p = 0.01
E(G) = €

Answer key

  1. 1. P = 0.05556
  2. 2. E(X) = 3.6
  3. 3. σ = 0.8367
  4. 4. Var(X) = 0.6475
  5. 5. P = 0.2787
  6. 6. E(G) = −1.5 €

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