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?200.35300.2400.15

The table gives the probability distribution of X, but one probability is missing. Find P(X = 10).

x: 10, 20, 30, 40p(x): ?, 0.35, 0.2, 0.15
P(X = 10) =
2.Easy
sum ≥ 7die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 7?

2 dice≥ 7
P =
3.Medium
n = 8k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 8? The order does not matter.

n = 8k = 2
N =
4.Medium
xp(x)00.320.340.1560.25μ = 2.7

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

x: 0, 2, 4, 6p(x): 0.3, 0.3, 0.15, 0.25
σ =
5.Hard
n = 11, p = 0.6: P(X = 1) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 1 correct answers?

n = 11p = 0.6k = 1
P =
6.Hard
€p(x)−30.8460.15270.01

A game costs €3 to play. You win €9 with probability 0.15 and €30 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€9: p = 0.15€30: p = 0.01
E(G) = €

Answer key

  1. 1. P(X = 10) = 0.3
  2. 2. P = 0.5833
  3. 3. N = 28
  4. 4. σ = 2.304
  5. 5. P = 0.0006921
  6. 6. E(G) = −1.35 €

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