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)00.120.340.2560.35

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

x: 0, 2, 4, 6p(x): 0.1, 0.3, 0.25, 0.35
E(X) =
2.Easy
sum = 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice= 11
P =
3.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
4.Medium
xp(x)10.220.330.340.2μ = 2.5

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

x: 1, 2, 3, 4p(x): 0.2, 0.3, 0.3, 0.2
Var(X) =
5.Hard
xp(x)00.3520.240.1560.3μ

X has the distribution shown, and Y = 2X + 5. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.35, 0.2, 0.15, 0.3Y = 2X + 5
σY =
6.Hard
n = 12, p = 0.25: P(X = 1) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 1 correct answers?

n = 12p = 0.25k = 1
P =

Answer key

  1. 1. E(X) = 3.7
  2. 2. P = 0.05556
  3. 3. P = 0.7209
  4. 4. Var(X) = 1.05
  5. 5. σY = 4.964
  6. 6. P = 0.1267

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