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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Name: ____________________   Date: ____________

1.Easy
sum ≥ 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 10?

2 dice≥ 10
P =
2.Easy
xp(x)100.25200.35300.05400.35

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

x: 10, 20, 30, 40p(x): 0.25, 0.35, 0.05, 0.35
E(X) =
3.Medium
xp(x)10.3520.130.2540.250.1μ = 2.6

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

x: 1, 2, 3, 4, 5p(x): 0.35, 0.1, 0.25, 0.2, 0.1
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
n = 10, p = 0.2: P(X ≤ 1) = ?k012345678910

10 components are tested, and each one fails with probability 0.2, independently. What is the probability P that at most one fails?

n = 10p = 0.2
P =
6.Hard
€p(x)−100.8400.151900.05

A game costs €10 to play. You win €50 with probability 0.15 and €200 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€50: p = 0.15€200: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.1667
  2. 2. E(X) = 25
  3. 3. σ = 1.393
  4. 4. P = 0.7209
  5. 5. P = 0.3758
  6. 6. E(G) = 7.5 €

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