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: 5blue: 2green: 4

A bag holds 5 red, 2 blue and 4 green balls. You draw one at random. What is the probability P that it is not red?

5 / 2 / 4
P =
2.Easy
xp(x)100.3200.25300.25400.2

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

x: 10, 20, 30, 40p(x): 0.3, 0.25, 0.25, 0.2
E(X) =
3.Medium
P(at least one six) = ??1?2P(six) = 1/6 on each roll

A fair die is rolled 2 times. What is the probability P of getting at least one six?

n = 2
P =
4.Medium
red: 4blue: 9

A bag holds 4 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

4 / 9
P =
5.Hard
n = 6, p = 0.6: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.6, independently. What is the probability P that at most one fails?

n = 6p = 0.6
P =
6.Hard
€p(x)−50.8150.152450.05

A game costs €5 to play. You win €20 with probability 0.15 and €250 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€20: p = 0.15€250: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.5455
  2. 2. E(X) = 23.5
  3. 3. P = 0.3056
  4. 4. P = 0.07692
  5. 5. P = 0.04096
  6. 6. E(G) = 10.5 €

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