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 = 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

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

A bag holds 3 red, 2 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

3 / 2 / 4
P =
3.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 =
4.Medium
xp(x)100.2200.3300.15400.35μ = 26.5

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

x: 10, 20, 30, 40p(x): 0.2, 0.3, 0.15, 0.35
Var(X) =
5.Hard
n = 8, p = 0.7: P(X = 1) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 1 correct answers?

n = 8p = 0.7k = 1
P =
6.Hard
n = 10, p = 0.25: P(X ≤ 1) = ?k012345678910

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

n = 10p = 0.25
P =

Answer key

  1. 1. P = 0.08333
  2. 2. P = 0.2222
  3. 3. P = 0.5981
  4. 4. Var(X) = 132.8
  5. 5. P = 0.001225
  6. 6. P = 0.244

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