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: 8blue: 7green: 5

A bag holds 8 red, 7 blue and 5 green balls. You draw one at random. What is the probability P that it is not red?

8 / 7 / 5
P =
2.Easy
sum = 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 3?

2 dice= 3
P =
3.Medium
xp(x)10.320.2530.140.35μ = 2.5

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

x: 1, 2, 3, 4p(x): 0.3, 0.25, 0.1, 0.35
σ =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7?8P(six) = 1/6 on each roll

A fair die is rolled 8 times. What is the probability P of getting at least one six?

n = 8
P =
5.Hard
xp(x)10.320.230.240.3μ

X has the distribution shown, and Y = 3X + 1. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.3, 0.2, 0.2, 0.3Y = 3X + 1
σY =
6.Hard
€p(x)−30.7530.2270.05

A game costs €3 to play. You win €6 with probability 0.2 and €30 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€6: p = 0.2€30: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.6
  2. 2. P = 0.05556
  3. 3. σ = 1.245
  4. 4. P = 0.7674
  5. 5. σY = 3.612
  6. 6. E(G) = −0.3 €

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