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)10.12?30.240.350.1

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 1, 2, 3, 4, 5p(x): 0.1, ?, 0.2, 0.3, 0.1
P(X = 2) =
2.Easy
xp(x)00.251?20.0530.35

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

x: 0, 1, 2, 3p(x): 0.25, ?, 0.05, 0.35
P(X = 1) =
3.Medium
xp(x)100.35200.35300.1400.2μ = 21.5

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

x: 10, 20, 30, 40p(x): 0.35, 0.35, 0.1, 0.2
Var(X) =
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
n = 7, p = 0.6: P(X = 4) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 4 correct answers?

n = 7p = 0.6k = 4
P =
6.Hard
€p(x)−20.7580.2980.05

A game costs €2 to play. You win €10 with probability 0.2 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 = €2€10: p = 0.2€100: p = 0.05
E(G) = €

Answer key

  1. 1. P(X = 2) = 0.3
  2. 2. P(X = 1) = 0.35
  3. 3. Var(X) = 122.8
  4. 4. N = 126
  5. 5. P = 0.2903
  6. 6. E(G) = 5 €

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