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 = 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 3?

2 dice= 3
P =
2.Easy
xp(x)00.110.2520.3530.0540.25

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 0, 1, 2, 3, 4p(x): 0.1, 0.25, 0.35, 0.05, 0.25
E(X) =
3.Medium
xp(x)100.35200.2300.1400.35μ = 24.5

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

x: 10, 20, 30, 40p(x): 0.35, 0.2, 0.1, 0.35
Var(X) =
4.Medium
red: 6blue: 9

A bag holds 6 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 9
P =
5.Hard
n = 9, p = 0.5: P(X = 2) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 2 correct answers?

n = 9p = 0.5k = 2
P =
6.Hard
n = 5, p = 0.2: P(X = 2) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 2 correct answers?

n = 5p = 0.2k = 2
P =

Answer key

  1. 1. P = 0.05556
  2. 2. E(X) = 2.1
  3. 3. Var(X) = 164.8
  4. 4. P = 0.1429
  5. 5. P = 0.07031
  6. 6. P = 0.2048

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