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: 6blue: 8green: 2

A bag holds 6 red, 8 blue and 2 green balls. You draw one at random. What is the probability P that it is blue?

6 / 8 / 2
P =
2.Easy
sum = 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice= 4
P =
3.Medium
xp(x)00.3520.1540.2560.25μ = 2.8

For the distribution shown, find the variance Var(X) of X.

x: 0, 2, 4, 6p(x): 0.35, 0.15, 0.25, 0.25
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
5.Hard
n = 9, p = 0.25: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 9p = 0.25
P =
6.Hard
xp(x)100.25200.1300.3400.35μ

X has the distribution shown, and Y = 10X + 5. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.25, 0.1, 0.3, 0.35Y = 10X + 5
σY =

Answer key

  1. 1. P = 0.5
  2. 2. P = 0.08333
  3. 3. Var(X) = 5.76
  4. 4. P = 0.5177
  5. 5. P = 0.3003
  6. 6. σY = 117.8

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