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 = 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 5?

2 dice= 5
P =
2.Easy
sum = 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice= 9
P =
3.Medium
xp(x)100.25200.3300.3400.15μ = 23.5

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

x: 10, 20, 30, 40p(x): 0.25, 0.3, 0.3, 0.15
σ =
4.Medium
xp(x)00.320.340.1560.25μ = 2.7

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

x: 0, 2, 4, 6p(x): 0.3, 0.3, 0.15, 0.25
Var(X) =
5.Hard
n = 8, p = 0.4: P(X = 3) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 3 correct answers?

n = 8p = 0.4k = 3
P =
6.Hard
n = 6, p = 0.1: P(X = 5) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 5 correct answers?

n = 6p = 0.1k = 5
P =

Answer key

  1. 1. P = 0.1111
  2. 2. P = 0.1111
  3. 3. σ = 10.14
  4. 4. Var(X) = 5.31
  5. 5. P = 0.2787
  6. 6. P = 5.4 × 10⁻⁵

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