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)00.0510.1520.230.340.3

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

x: 0, 1, 2, 3, 4p(x): 0.05, 0.15, 0.2, 0.3, 0.3
E(X) =
2.Easy
xp(x)100.1520?300.35400.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 20).

x: 10, 20, 30, 40p(x): 0.15, ?, 0.35, 0.3
P(X = 20) =
3.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 =
4.Medium
n = 9k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 9? The order does not matter.

n = 9k = 5
N =
5.Hard
€p(x)−30.6590.3270.05

A game costs €3 to play. You win €12 with probability 0.3 and €30 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€12: p = 0.3€30: p = 0.05
E(G) = €
6.Hard
€p(x)−100.74400.254900.01

A game costs €10 to play. You win €50 with probability 0.25 and €500 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€50: p = 0.25€500: p = 0.01
E(G) = €

Answer key

  1. 1. E(X) = 2.65
  2. 2. P(X = 20) = 0.2
  3. 3. N = 495
  4. 4. N = 126
  5. 5. E(G) = 2.1 €
  6. 6. E(G) = 7.5 €

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