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: 4blue: 6green: 2

A bag holds 4 red, 6 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

4 / 6 / 2
P =
2.Easy
red: 4blue: 3green: 4

A bag holds 4 red, 3 blue and 4 green balls. You draw one at random. What is the probability P that it is red?

4 / 3 / 4
P =
3.Medium
xp(x)10.320.330.3540.05μ = 2.15

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

x: 1, 2, 3, 4p(x): 0.3, 0.3, 0.35, 0.05
σ =
4.Medium
red: 5blue: 6

A bag holds 5 red and 6 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 6
P =
5.Hard
€p(x)−20.6880.3380.02

A game costs €2 to play. You win €10 with probability 0.3 and €40 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€10: p = 0.3€40: p = 0.02
E(G) = €
6.Hard
n = 7, p = 0.3: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.3, independently. What is the probability P that at most one fails?

n = 7p = 0.3
P =

Answer key

  1. 1. P = 0.3333
  2. 2. P = 0.3636
  3. 3. σ = 0.9097
  4. 4. P = 0.1818
  5. 5. E(G) = 1.8 €
  6. 6. P = 0.3294

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