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)10.0520.2530.1540.3550.2

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

x: 1, 2, 3, 4, 5p(x): 0.05, 0.25, 0.15, 0.35, 0.2
E(X) =
2.Easy
xp(x)100.15200.35300.1540?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 40).

x: 10, 20, 30, 40p(x): 0.15, 0.35, 0.15, ?
P(X = 40) =
3.Medium
n = 7k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 7? The order does not matter.

n = 7k = 5
N =
4.Medium
xp(x)100.1200.35300.3400.25μ = 27

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

x: 10, 20, 30, 40p(x): 0.1, 0.35, 0.3, 0.25
Var(X) =
5.Hard
€p(x)−30.88120.11470.02

A game costs €3 to play. You win €15 with probability 0.1 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 = 0.1€150: p = 0.02
E(G) = €
6.Hard
n = 11, p = 0.2: P(X = 5) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 5 correct answers?

n = 11p = 0.2k = 5
P =

Answer key

  1. 1. E(X) = 3.4
  2. 2. P(X = 40) = 0.35
  3. 3. N = 21
  4. 4. Var(X) = 91
  5. 5. E(G) = 1.5 €
  6. 6. P = 0.03876

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