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
red: 2blue: 3

A bag holds 2 red and 3 blue balls. You draw one at random. What is the probability P that it is not red?

2 / 3
P =
2.Easy
xp(x)10.1520.1530.3540.35

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

x: 1, 2, 3, 4p(x): 0.15, 0.15, 0.35, 0.35
E(X) =
3.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
5.Hard
€p(x)−20.7980.2380.01

A game costs €2 to play. You win €10 with probability 0.2 and €40 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€10: p = 0.2€40: p = 0.01
E(G) = €
6.Hard
n = 11, p = 0.2: P(X ≤ 1) = ?k01234567891011

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

n = 11p = 0.2
P =

Answer key

  1. 1. P = 0.6
  2. 2. E(X) = 2.9
  3. 3. Var(X) = 0.7
  4. 4. P = 0.5177
  5. 5. E(G) = 0.4 €
  6. 6. P = 0.3221

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