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 ≥ 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 11?

2 dice≥ 11
P =
2.Easy
xp(x)10.320.230.140.2550.15

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.2, 0.1, 0.25, 0.15
E(X) =
3.Medium
n = 12k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 12? The order does not matter.

n = 12k = 5
N =
4.Medium
P(at least one six) = ??1?2?3?4?5?6P(six) = 1/6 on each roll

A fair die is rolled 6 times. What is the probability P of getting at least one six?

n = 6
P =
5.Hard
n = 8, p = 0.2: P(X = 2) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 2 correct answers?

n = 8p = 0.2k = 2
P =
6.Hard
xp(x)100.15200.25300.25400.35μ

X has the distribution shown, and Y = 0.5X − 3. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.15, 0.25, 0.25, 0.35Y = 0.5X − 3
σY =

Answer key

  1. 1. P = 0.08333
  2. 2. E(X) = 2.75
  3. 3. N = 792
  4. 4. P = 0.6651
  5. 5. P = 0.2936
  6. 6. σY = 5.385

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