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
sum = 6die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 6?

2 dice= 6
P =
2.Easy
red: 5blue: 3green: 2

A bag holds 5 red, 3 blue and 2 green balls. You draw one at random. What is the probability P that it is blue?

5 / 3 / 2
P =
3.Medium
xp(x)00.320.1540.360.25μ = 3

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

x: 0, 2, 4, 6p(x): 0.3, 0.15, 0.3, 0.25
σ =
4.Medium
P(at least one six) = ??1?2?3?4?5P(six) = 1/6 on each roll

A fair die is rolled 5 times. What is the probability P of getting at least one six?

n = 5
P =
5.Hard
xp(x)00.3510.3520.230.1μ

X has the distribution shown, and Y = 5X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.35, 0.35, 0.2, 0.1Y = 5X + 5
σY =
6.Hard
n = 5, p = 0.7: P(X ≤ 1) = ?k012345

5 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 5p = 0.7
P =

Answer key

  1. 1. P = 0.1389
  2. 2. P = 0.3
  3. 3. σ = 2.324
  4. 4. P = 0.5981
  5. 5. σY = 4.867
  6. 6. P = 0.03078

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