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
red: 2blue: 4green: 3

A bag holds 2 red, 4 blue and 3 green balls. You draw one at random. What is the probability P that it is blue?

2 / 4 / 3
P =
2.Easy
xp(x)00.310.1520.253?40.05

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 0, 1, 2, 3, 4p(x): 0.3, 0.15, 0.25, ?, 0.05
P(X = 3) =
3.Medium
red: 3blue: 5

A bag holds 3 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 5
P =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7?8P(six) = 1/6 on each roll

A fair die is rolled 8 times. What is the probability P of getting at least one six?

n = 8
P =
5.Hard
n = 5, p = 0.4: P(X = 2) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 2 correct answers?

n = 5p = 0.4k = 2
P =
6.Hard
€p(x)−30.6830.3270.02

A game costs €3 to play. You win €6 with probability 0.3 and €30 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€6: p = 0.3€30: p = 0.02
E(G) = €

Answer key

  1. 1. P = 0.4444
  2. 2. P(X = 3) = 0.25
  3. 3. P = 0.1071
  4. 4. P = 0.7674
  5. 5. P = 0.3456
  6. 6. E(G) = −0.6 €

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