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)0?10.3520.35

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

x: 0, 1, 2p(x): ?, 0.35, 0.35
P(X = 0) =
2.Easy
xp(x)00.3510.352?

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

x: 0, 1, 2p(x): 0.35, 0.35, ?
P(X = 2) =
3.Medium
xp(x)10.0520.330.1540.1550.35μ = 3.45

For the distribution shown, find the standard deviation σ of X.

x: 1, 2, 3, 4, 5p(x): 0.05, 0.3, 0.15, 0.15, 0.35
σ =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
5.Hard
€p(x)−30.7390.25570.02

A game costs €3 to play. You win €12 with probability 0.25 and €60 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€12: p = 0.25€60: p = 0.02
E(G) = €
6.Hard
€p(x)−100.75200.24900.05

A game costs €10 to play. You win €30 with probability 0.2 and €500 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€30: p = 0.2€500: p = 0.05
E(G) = €

Answer key

  1. 1. P(X = 0) = 0.3
  2. 2. P(X = 2) = 0.3
  3. 3. σ = 1.359
  4. 4. P = 0.7209
  5. 5. E(G) = 1.2 €
  6. 6. E(G) = 21 €

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