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
xp(x)100.25200.25300.3400.2

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

x: 10, 20, 30, 40p(x): 0.25, 0.25, 0.3, 0.2
E(X) =
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
red: 7blue: 5

A bag holds 7 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 5
P =
4.Medium
n = 15k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 15? The order does not matter.

n = 15k = 2
N =
5.Hard
€p(x)−30.8960.1570.01

A game costs €3 to play. You win €9 with probability 0.1 and €60 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€9: p = 0.1€60: p = 0.01
E(G) = €
6.Hard
n = 6, p = 0.4: P(X = 5) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 5 correct answers?

n = 6p = 0.4k = 5
P =

Answer key

  1. 1. E(X) = 24.5
  2. 2. P = 0.1111
  3. 3. P = 0.3182
  4. 4. N = 105
  5. 5. E(G) = −1.5 €
  6. 6. P = 0.03686

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