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)00.21?20.330.35

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

x: 0, 1, 2, 3p(x): 0.2, ?, 0.3, 0.35
P(X = 1) =
2.Easy
xp(x)00.220.340.260.3

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

x: 0, 2, 4, 6p(x): 0.2, 0.3, 0.2, 0.3
E(X) =
3.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 =
4.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 =
5.Hard
€p(x)−50.78150.2950.02

A game costs €5 to play. You win €20 with probability 0.2 and €100 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€20: p = 0.2€100: p = 0.02
E(G) = €
6.Hard
n = 10, p = 0.4: P(X ≤ 1) = ?k012345678910

10 components are tested, and each one fails with probability 0.4, independently. What is the probability P that at most one fails?

n = 10p = 0.4
P =

Answer key

  1. 1. P(X = 1) = 0.15
  2. 2. E(X) = 3.2
  3. 3. P = 0.6651
  4. 4. P = 0.3056
  5. 5. E(G) = 1 €
  6. 6. P = 0.04636

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