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)10.220.130.1540.350.25

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, 0.15, 0.3, 0.25
E(X) =
2.Easy
sum = 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 3?

2 dice= 3
P =
3.Medium
xp(x)00.3510.0520.2530.35μ = 1.6

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

x: 0, 1, 2, 3p(x): 0.35, 0.05, 0.25, 0.35
σ =
4.Medium
red: 7blue: 4

A bag holds 7 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 4
P =
5.Hard
xp(x)10.120.3530.2540.3μ

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

x: 1, 2, 3, 4p(x): 0.1, 0.35, 0.25, 0.3Y = 0.5X − 3
σY =
6.Hard
n = 6, p = 0.4: P(X = 1) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 1 correct answers?

n = 6p = 0.4k = 1
P =

Answer key

  1. 1. E(X) = 3.3
  2. 2. P = 0.05556
  3. 3. σ = 1.281
  4. 4. P = 0.3818
  5. 5. σY = 0.4969
  6. 6. P = 0.1866

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