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)10.220.130.340.250.2

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.1, 0.3, 0.2, 0.2
E(X) =
2.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 =
3.Medium
P(at least one six) = ??1?2?3?4?5P(six) = 1/6 on each roll

A fair die is rolled 5 times. What is the probability P of getting at least one six?

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

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
5.Hard
xp(x)10.0520.330.240.3550.1μ

X has the distribution shown, and Y = 10X + 20. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.05, 0.3, 0.2, 0.35, 0.1Y = 10X + 20
σY =
6.Hard
n = 9, p = 0.3: P(X = 5) = ?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 5 correct answers?

n = 9p = 0.3k = 5
P =

Answer key

  1. 1. E(X) = 3.1
  2. 2. P = 0.08333
  3. 3. P = 0.5981
  4. 4. P = 0.5177
  5. 5. σY = 11.08
  6. 6. P = 0.07351

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