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 = 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 4?

2 dice= 4
P =
2.Easy
sum ≥ 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice≥ 3
P =
3.Medium
n = 13k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 13? The order does not matter.

n = 13k = 4
N =
4.Medium
P(at least one six) = ??1?2?3?4?5?6P(six) = 1/6 on each roll

A fair die is rolled 6 times. What is the probability P of getting at least one six?

n = 6
P =
5.Hard
€p(x)−50.83200.15450.02

A game costs €5 to play. You win €25 with probability 0.15 and €50 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€25: p = 0.15€50: p = 0.02
E(G) = €
6.Hard
n = 5, p = 0.6: P(X = 1) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 1 correct answers?

n = 5p = 0.6k = 1
P =

Answer key

  1. 1. P = 0.08333
  2. 2. P = 0.9722
  3. 3. N = 715
  4. 4. P = 0.6651
  5. 5. E(G) = −0.25 €
  6. 6. P = 0.0768

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