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)00.052?40.3560.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 2, 4, 6p(x): 0.05, ?, 0.35, 0.25
P(X = 2) =
2.Easy
xp(x)00.210.220.330.1540.15

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

x: 0, 1, 2, 3, 4p(x): 0.2, 0.2, 0.3, 0.15, 0.15
E(X) =
3.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 =
4.Medium
xp(x)10.2520.330.2540.2μ = 2.4

For the distribution shown, find the variance Var(X) of X.

x: 1, 2, 3, 4p(x): 0.25, 0.3, 0.25, 0.2
Var(X) =
5.Hard
€p(x)−100.88100.1900.02

A game costs €10 to play. You win €20 with probability 0.1 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 = €10€20: p = 0.1€100: p = 0.02
E(G) = €
6.Hard
€p(x)−20.6840.3380.02

A game costs €2 to play. You win €6 with probability 0.3 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€6: p = 0.3€40: p = 0.02
E(G) = €

Answer key

  1. 1. P(X = 2) = 0.35
  2. 2. E(X) = 1.85
  3. 3. P = 0.7674
  4. 4. Var(X) = 1.14
  5. 5. E(G) = −6 €
  6. 6. E(G) = 0.6 €

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