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)10.352?30.340.15

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

x: 1, 2, 3, 4p(x): 0.35, ?, 0.3, 0.15
P(X = 2) =
2.Easy
red: 5blue: 6green: 3

A bag holds 5 red, 6 blue and 3 green balls. You draw one at random. What is the probability P that it is blue?

5 / 6 / 3
P =
3.Medium
xp(x)00.3510.120.2530.3μ = 1.5

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

x: 0, 1, 2, 3p(x): 0.35, 0.1, 0.25, 0.3
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)−50.7350.252450.02

A game costs €5 to play. You win €10 with probability 0.25 and €250 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€10: p = 0.25€250: p = 0.02
E(G) = €
6.Hard
€p(x)−30.73120.251470.02

A game costs €3 to play. You win €15 with probability 0.25 and €150 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€15: p = 0.25€150: p = 0.02
E(G) = €

Answer key

  1. 1. P(X = 2) = 0.2
  2. 2. P = 0.4286
  3. 3. σ = 1.245
  4. 4. P = 0.7209
  5. 5. E(G) = 2.5 €
  6. 6. E(G) = 3.75 €

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