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)0?10.220.1530.2540.05

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 1, 2, 3, 4p(x): ?, 0.2, 0.15, 0.25, 0.05
P(X = 0) =
2.Easy
xp(x)10.2520.353?40.1

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 1, 2, 3, 4p(x): 0.25, 0.35, ?, 0.1
P(X = 3) =
3.Medium
n = 9k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 9? The order does not matter.

n = 9k = 4
N =
4.Medium
xp(x)10.320.130.240.350.1μ = 2.8

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.1, 0.2, 0.3, 0.1
Var(X) =
5.Hard
n = 9, p = 0.3: P(X = 1) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 1 correct answers?

n = 9p = 0.3k = 1
P =
6.Hard
€p(x)−100.89200.14900.01

A game costs €10 to play. You win €30 with probability 0.1 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€30: p = 0.1€500: p = 0.01
E(G) = €

Answer key

  1. 1. P(X = 0) = 0.35
  2. 2. P(X = 3) = 0.3
  3. 3. N = 126
  4. 4. Var(X) = 1.96
  5. 5. P = 0.1556
  6. 6. E(G) = −2 €

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