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)100.05200.35300.25400.35

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

x: 10, 20, 30, 40p(x): 0.05, 0.35, 0.25, 0.35
E(X) =
2.Easy
xp(x)100.3200.2530?400.2

The table gives the probability distribution of X, but one probability is missing. Find P(X = 30).

x: 10, 20, 30, 40p(x): 0.3, 0.25, ?, 0.2
P(X = 30) =
3.Medium
xp(x)10.120.1530.3540.250.2μ = 3.25

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

x: 1, 2, 3, 4, 5p(x): 0.1, 0.15, 0.35, 0.2, 0.2
σ =
4.Medium
n = 12k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 12? The order does not matter.

n = 12k = 4
N =
5.Hard
€p(x)−10.8940.1190.01

A game costs €1 to play. You win €5 with probability 0.1 and €20 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 = 0.1€20: p = 0.01
E(G) = €
6.Hard
€p(x)−50.8550.1950.05

A game costs €5 to play. You win €10 with probability 0.1 and €100 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€10: p = 0.1€100: p = 0.05
E(G) = €

Answer key

  1. 1. E(X) = 29
  2. 2. P(X = 30) = 0.25
  3. 3. σ = 1.22
  4. 4. N = 495
  5. 5. E(G) = −0.3 €
  6. 6. E(G) = 1 €

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