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
sum ≥ 8die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 8?

2 dice≥ 8
P =
2.Easy
xp(x)10.2520.2530.3540.15

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

x: 1, 2, 3, 4p(x): 0.25, 0.25, 0.35, 0.15
E(X) =
3.Medium
n = 15k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 15? The order does not matter.

n = 15k = 2
N =
4.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
5.Hard
€p(x)−10.7420.25190.01

A game costs €1 to play. You win €3 with probability 0.25 and €20 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€3: p = 0.25€20: p = 0.01
E(G) = €
6.Hard
xp(x)100.35200.1300.2400.35μ

X has the distribution shown, and Y = 3X − 3. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.35, 0.1, 0.2, 0.35Y = 3X − 3
σY =

Answer key

  1. 1. P = 0.4167
  2. 2. E(X) = 2.4
  3. 3. N = 105
  4. 4. Var(X) = 0.6475
  5. 5. E(G) = −0.05 €
  6. 6. σY = 38.51

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