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)00.351?20.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2p(x): 0.35, ?, 0.35
P(X = 1) =
2.Easy
red: 5blue: 3green: 3

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

5 / 3 / 3
P =
3.Medium
xp(x)00.2520.3540.0560.35μ = 3

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

x: 0, 2, 4, 6p(x): 0.25, 0.35, 0.05, 0.35
Var(X) =
4.Medium
red: 7blue: 4

A bag holds 7 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 4
P =
5.Hard
xp(x)100.2200.25300.25400.3μ

X has the distribution shown, and Y = 5X + 20. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.2, 0.25, 0.25, 0.3Y = 5X + 20
σY =
6.Hard
€p(x)−10.6940.3490.01

A game costs €1 to play. You win €5 with probability 0.3 and €50 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€5: p = 0.3€50: p = 0.01
E(G) = €

Answer key

  1. 1. P(X = 1) = 0.3
  2. 2. P = 0.4545
  3. 3. Var(X) = 5.8
  4. 4. P = 0.3818
  5. 5. σY = 55.4
  6. 6. E(G) = 1 €

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