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: 8green: 5

A bag holds 4 red, 8 blue and 5 green balls. You draw one at random. What is the probability P that it is not red?

4 / 8 / 5
P =
2.Easy
sum ≥ 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 4?

2 dice≥ 4
P =
3.Medium
P(at least one six) = ??1?2?3P(six) = 1/6 on each roll

A fair die is rolled 3 times. What is the probability P of getting at least one six?

n = 3
P =
4.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 =
5.Hard
xp(x)00.320.3540.360.05μ

X has the distribution shown, and Y = 2X + 20. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.3, 0.35, 0.3, 0.05Y = 2X + 20
σY =
6.Hard
€p(x)−50.7100.25950.05

A game costs €5 to play. You win €15 with probability 0.25 and €100 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€15: p = 0.25€100: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.7647
  2. 2. P = 0.9167
  3. 3. P = 0.4213
  4. 4. P = 0.175
  5. 5. σY = 3.555
  6. 6. E(G) = 3.75 €

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