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 = 6die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 6?

2 dice= 6
P =
2.Easy
xp(x)00.252?40.2560.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 2, 4, 6p(x): 0.25, ?, 0.25, 0.25
P(X = 2) =
3.Medium
xp(x)00.3510.320.2530.1μ = 1.1

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

x: 0, 1, 2, 3p(x): 0.35, 0.3, 0.25, 0.1
Var(X) =
4.Medium
red: 4blue: 4

A bag holds 4 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

4 / 4
P =
5.Hard
€p(x)−100.73200.25900.02

A game costs €10 to play. You win €30 with probability 0.25 and €100 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€30: p = 0.25€100: p = 0.02
E(G) = €
6.Hard
n = 9, p = 0.6: P(X = 1) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 1 correct answers?

n = 9p = 0.6k = 1
P =

Answer key

  1. 1. P = 0.1389
  2. 2. P(X = 2) = 0.25
  3. 3. Var(X) = 0.99
  4. 4. P = 0.2143
  5. 5. E(G) = −0.5 €
  6. 6. P = 0.003539

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