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: 8green: 4

A bag holds 2 red, 8 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

2 / 8 / 4
P =
2.Easy
xp(x)100.3200.330?400.15

The table gives the probability distribution of X, but one probability is missing. Find P(X = 30).

x: 10, 20, 30, 40p(x): 0.3, 0.3, ?, 0.15
P(X = 30) =
3.Medium
xp(x)100.2200.25300.35400.2μ = 25.5

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

x: 10, 20, 30, 40p(x): 0.2, 0.25, 0.35, 0.2
Var(X) =
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)−20.8340.15180.02

A game costs €2 to play. You win €6 with probability 0.15 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 = €2€6: p = 0.15€20: p = 0.02
E(G) = €
6.Hard
n = 10, p = 0.25: P(X = 4) = ?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 4 correct answers?

n = 10p = 0.25k = 4
P =

Answer key

  1. 1. P = 0.5714
  2. 2. P(X = 30) = 0.25
  3. 3. Var(X) = 104.8
  4. 4. P = 0.5177
  5. 5. E(G) = −0.7 €
  6. 6. P = 0.146

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