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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
xp(x)00.320.140.356?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 6).

x: 0, 2, 4, 6p(x): 0.3, 0.1, 0.35, ?
P(X = 6) =
2.Easy
xp(x)00.1520.340.3560.2

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

x: 0, 2, 4, 6p(x): 0.15, 0.3, 0.35, 0.2
E(X) =
3.Medium
xp(x)10.120.2530.3540.3μ = 2.85

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

x: 1, 2, 3, 4p(x): 0.1, 0.25, 0.35, 0.3
σ =
4.Medium
n = 6k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 6? The order does not matter.

n = 6k = 4
N =
5.Hard
€p(x)−50.73200.25950.02

A game costs €5 to play. You win €25 with probability 0.25 and €100 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€25: p = 0.25€100: p = 0.02
E(G) = €
6.Hard
€p(x)−30.8490.15570.01

A game costs €3 to play. You win €12 with probability 0.15 and €60 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€12: p = 0.15€60: p = 0.01
E(G) = €

Answer key

  1. 1. P(X = 6) = 0.25
  2. 2. E(X) = 3.2
  3. 3. σ = 0.9631
  4. 4. N = 15
  5. 5. E(G) = 3.25 €
  6. 6. E(G) = −0.6 €

Full step-by-step solutions: practise this topic on examproblems.com.