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: 8blue: 5green: 4

A bag holds 8 red, 5 blue and 4 green balls. You draw one at random. What is the probability P that it is red?

8 / 5 / 4
P =
2.Easy
sum ≥ 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 9?

2 dice≥ 9
P =
3.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
σ =
4.Medium
xp(x)100.15200.35300.35400.15μ = 25

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

x: 10, 20, 30, 40p(x): 0.15, 0.35, 0.35, 0.15
Var(X) =
5.Hard
n = 12, p = 0.25: P(X ≤ 1) = ?k0123456789101112

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

n = 12p = 0.25
P =
6.Hard
n = 7, p = 0.3: P(X = 5) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 5 correct answers?

n = 7p = 0.3k = 5
P =

Answer key

  1. 1. P = 0.4706
  2. 2. P = 0.2778
  3. 3. σ = 0.8367
  4. 4. Var(X) = 85
  5. 5. P = 0.1584
  6. 6. P = 0.025

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