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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Name: ____________________   Date: ____________

1.Easy
sum = 6die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 6?

2 dice= 6
P =
2.Easy
xp(x)00.1510.120.1530.340.3

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

x: 0, 1, 2, 3, 4p(x): 0.15, 0.1, 0.15, 0.3, 0.3
E(X) =
3.Medium
xp(x)00.220.240.360.3μ = 3.4

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

x: 0, 2, 4, 6p(x): 0.2, 0.2, 0.3, 0.3
σ =
4.Medium
P(at least one six) = ??1?2?3P(six) = 1/6 on each roll

A fair die is rolled 3 times. What is the probability P of getting at least one six?

n = 3
P =
5.Hard
n = 12, p = 0.7: P(X = 3) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 3 correct answers?

n = 12p = 0.7k = 3
P =
6.Hard
xp(x)00.3520.340.1560.2μ

X has the distribution shown, and Y = 5X + 4. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.35, 0.3, 0.15, 0.2Y = 5X + 4
σY =

Answer key

  1. 1. P = 0.1389
  2. 2. E(X) = 2.5
  3. 3. σ = 2.2
  4. 4. P = 0.4213
  5. 5. P = 0.001485
  6. 6. σY = 11.22

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