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
red: 6blue: 5

A bag holds 6 red and 5 blue balls. You draw one at random. What is the probability P that it is red?

6 / 5
P =
2.Easy
red: 8blue: 6green: 1

A bag holds 8 red, 6 blue and 1 green balls. You draw one at random. What is the probability P that it is red?

8 / 6 / 1
P =
3.Medium
xp(x)10.320.3530.240.15μ = 2.2

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

x: 1, 2, 3, 4p(x): 0.3, 0.35, 0.2, 0.15
σ =
4.Medium
xp(x)00.310.3520.35μ = 1.05

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
Var(X) =
5.Hard
€p(x)−10.7310.25190.02

A game costs €1 to play. You win €2 with probability 0.25 and €20 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€2: p = 0.25€20: p = 0.02
E(G) = €
6.Hard
n = 12, p = 0.4: P(X = 4) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 4 correct answers?

n = 12p = 0.4k = 4
P =

Answer key

  1. 1. P = 0.5455
  2. 2. P = 0.5333
  3. 3. σ = 1.03
  4. 4. Var(X) = 0.6475
  5. 5. E(G) = −0.1 €
  6. 6. P = 0.2128

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