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: 2blue: 4

A bag holds 2 red and 4 blue balls. You draw one at random. What is the probability P that it is blue?

2 / 4
P =
2.Easy
xp(x)00.1520.240.36?

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

x: 0, 2, 4, 6p(x): 0.15, 0.2, 0.3, ?
P(X = 6) =
3.Medium
xp(x)00.2510.1520.330.3μ = 1.65

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

x: 0, 1, 2, 3p(x): 0.25, 0.15, 0.3, 0.3
σ =
4.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
5.Hard
€p(x)−30.6590.3570.05

A game costs €3 to play. You win €12 with probability 0.3 and €60 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€12: p = 0.3€60: p = 0.05
E(G) = €
6.Hard
n = 10, p = 0.25: P(X = 1) = ?k012345678910

A test has 10 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 = 10p = 0.25k = 1
P =

Answer key

  1. 1. P = 0.6667
  2. 2. P(X = 6) = 0.35
  3. 3. σ = 1.152
  4. 4. P = 0.5177
  5. 5. E(G) = 3.6 €
  6. 6. P = 0.1877

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