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 at least 6?

2 dice≥ 6
P =
2.Easy
red: 4blue: 2green: 3

A bag holds 4 red, 2 blue and 3 green balls. You draw one at random. What is the probability P that it is not red?

4 / 2 / 3
P =
3.Medium
xp(x)00.310.3520.35μ = 1.05

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
Var(X) =
4.Medium
red: 4blue: 9

A bag holds 4 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

4 / 9
P =
5.Hard
xp(x)00.310.3520.35μ

X has the distribution shown, and Y = 5X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.3, 0.35, 0.35Y = 5X + 1
σY =
6.Hard
n = 11, p = 0.1: P(X = 3) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 3 correct answers?

n = 11p = 0.1k = 3
P =

Answer key

  1. 1. P = 0.7222
  2. 2. P = 0.5556
  3. 3. Var(X) = 0.6475
  4. 4. P = 0.07692
  5. 5. σY = 4.023
  6. 6. P = 0.07103

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