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)10.0520.330.3540.2550.05

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

x: 1, 2, 3, 4, 5p(x): 0.05, 0.3, 0.35, 0.25, 0.05
E(X) =
2.Easy
red: 3blue: 8green: 4

A bag holds 3 red, 8 blue and 4 green balls. You draw one at random. What is the probability P that it is not red?

3 / 8 / 4
P =
3.Medium
P(at least one six) = ??1?2P(six) = 1/6 on each roll

A fair die is rolled 2 times. What is the probability P of getting at least one six?

n = 2
P =
4.Medium
n = 8k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 8? The order does not matter.

n = 8k = 2
N =
5.Hard
n = 9, p = 0.3: P(X = 3) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 3 correct answers?

n = 9p = 0.3k = 3
P =
6.Hard
€p(x)−30.8930.1570.01

A game costs €3 to play. You win €6 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€6: p = 0.1€60: p = 0.01
E(G) = €

Answer key

  1. 1. E(X) = 2.95
  2. 2. P = 0.8
  3. 3. P = 0.3056
  4. 4. N = 28
  5. 5. P = 0.2668
  6. 6. E(G) = −1.8 €

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