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: 5blue: 4green: 2

A bag holds 5 red, 4 blue and 2 green balls. You draw one at random. What is the probability P that it is not red?

5 / 4 / 2
P =
2.Easy
sum = 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 9?

2 dice= 9
P =
3.Medium
red: 7blue: 9

A bag holds 7 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 9
P =
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)10.120.2530.3540.3μ

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

x: 1, 2, 3, 4p(x): 0.1, 0.25, 0.35, 0.3Y = 3X + 1
σY =
6.Hard
€p(x)−50.65150.3450.05

A game costs €5 to play. You win €20 with probability 0.3 and €50 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€20: p = 0.3€50: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.5455
  2. 2. P = 0.1111
  3. 3. P = 0.175
  4. 4. P = 0.7674
  5. 5. σY = 2.889
  6. 6. E(G) = 3.5 €

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