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 = 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice= 3
P =
2.Easy
red: 4blue: 4green: 2

A bag holds 4 red, 4 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

4 / 4 / 2
P =
3.Medium
xp(x)10.120.330.2540.250.15μ = 3

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

x: 1, 2, 3, 4, 5p(x): 0.1, 0.3, 0.25, 0.2, 0.15
Var(X) =
4.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 =
5.Hard
n = 11, p = 0.4: P(X ≤ 1) = ?k01234567891011

11 components are tested, and each one fails with probability 0.4, independently. What is the probability P that at most one fails?

n = 11p = 0.4
P =
6.Hard
n = 10, p = 0.7: P(X = 5) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 5 correct answers?

n = 10p = 0.7k = 5
P =

Answer key

  1. 1. P = 0.05556
  2. 2. P = 0.4
  3. 3. Var(X) = 1.5
  4. 4. P = 0.4213
  5. 5. P = 0.03023
  6. 6. P = 0.1029

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