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)00.351?20.230.2

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2, 3p(x): 0.35, ?, 0.2, 0.2
P(X = 1) =
2.Easy
xp(x)0?10.3520.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 1, 2p(x): ?, 0.35, 0.3
P(X = 0) =
3.Medium
P(at least one six) = ??1?2?3?4?5P(six) = 1/6 on each roll

A fair die is rolled 5 times. What is the probability P of getting at least one six?

n = 5
P =
4.Medium
red: 3blue: 6

A bag holds 3 red and 6 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 6
P =
5.Hard
n = 12, p = 0.1: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.1, independently. What is the probability P that at most one fails?

n = 12p = 0.1
P =
6.Hard
€p(x)−20.7320.25380.02

A game costs €2 to play. You win €4 with probability 0.25 and €40 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€4: p = 0.25€40: p = 0.02
E(G) = €

Answer key

  1. 1. P(X = 1) = 0.25
  2. 2. P(X = 0) = 0.35
  3. 3. P = 0.5981
  4. 4. P = 0.08333
  5. 5. P = 0.659
  6. 6. E(G) = −0.2 €

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