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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1.Easy
sum = 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 11?

2 dice= 11
P =
2.Easy
xp(x)00.310.052?30.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 1, 2, 3p(x): 0.3, 0.05, ?, 0.3
P(X = 2) =
3.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
4.Medium
red: 5blue: 4

A bag holds 5 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 4
P =
5.Hard
n = 6, p = 0.7: P(X = 4) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 4 correct answers?

n = 6p = 0.7k = 4
P =
6.Hard
n = 5, p = 0.7: P(X = 1) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 1 correct answers?

n = 5p = 0.7k = 1
P =

Answer key

  1. 1. P = 0.05556
  2. 2. P(X = 2) = 0.35
  3. 3. P = 0.5177
  4. 4. P = 0.2778
  5. 5. P = 0.3241
  6. 6. P = 0.02835

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