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 ≥ 8die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 8?

2 dice≥ 8
P =
2.Easy
xp(x)00.21?20.230.240.2

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2, 3, 4p(x): 0.2, ?, 0.2, 0.2, 0.2
P(X = 1) =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
σ =
4.Medium
red: 5blue: 3

A bag holds 5 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 3
P =
5.Hard
n = 8, p = 0.25: P(X = 4) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 4 correct answers?

n = 8p = 0.25k = 4
P =
6.Hard
n = 8, p = 0.4: P(X ≤ 1) = ?k012345678

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

n = 8p = 0.4
P =

Answer key

  1. 1. P = 0.4167
  2. 2. P(X = 1) = 0.2
  3. 3. σ = 0.8047
  4. 4. P = 0.3571
  5. 5. P = 0.08652
  6. 6. P = 0.1064

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