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 = 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 4?

2 dice= 4
P =
2.Easy
xp(x)00.220.3540.356?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 6).

x: 0, 2, 4, 6p(x): 0.2, 0.35, 0.35, ?
P(X = 6) =
3.Medium
red: 3blue: 9

A bag holds 3 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 9
P =
4.Medium
xp(x)00.2510.3520.230.2μ = 1.35

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

x: 0, 1, 2, 3p(x): 0.25, 0.35, 0.2, 0.2
Var(X) =
5.Hard
n = 8, p = 0.6: P(X = 1) = ?k012345678

A test has 8 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 = 8p = 0.6k = 1
P =
6.Hard
€p(x)−10.6540.3490.05

A game costs €1 to play. You win €5 with probability 0.3 and €50 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€5: p = 0.3€50: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.08333
  2. 2. P(X = 6) = 0.1
  3. 3. P = 0.04545
  4. 4. Var(X) = 1.127
  5. 5. P = 0.007864
  6. 6. E(G) = 3 €

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