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)10.220.230.254?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 1, 2, 3, 4p(x): 0.2, 0.2, 0.25, ?
P(X = 4) =
2.Easy
xp(x)00.210.320.3530.15

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

x: 0, 1, 2, 3p(x): 0.2, 0.3, 0.35, 0.15
E(X) =
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
P(at least one six) = ??1?2?3P(six) = 1/6 on each roll

A fair die is rolled 3 times. What is the probability P of getting at least one six?

n = 3
P =
5.Hard
€p(x)−30.8930.1270.01

A game costs €3 to play. You win €6 with probability 0.1 and €30 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€30: p = 0.01
E(G) = €
6.Hard
€p(x)−50.8350.15950.02

A game costs €5 to play. You win €10 with probability 0.15 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€10: p = 0.15€100: p = 0.02
E(G) = €

Answer key

  1. 1. P(X = 4) = 0.35
  2. 2. E(X) = 1.45
  3. 3. P = 0.5981
  4. 4. P = 0.4213
  5. 5. E(G) = −2.1 €
  6. 6. E(G) = −1.5 €

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