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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
sum = 7die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 7?

2 dice= 7
P =
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
P(at least one six) = ??1?2P(six) = 1/6 on each roll

A fair die is rolled 2 times. What is the probability P of getting at least one six?

n = 2
P =
4.Medium
xp(x)00.1510.120.130.340.35μ = 2.6

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

x: 0, 1, 2, 3, 4p(x): 0.15, 0.1, 0.1, 0.3, 0.35
Var(X) =
5.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = 10X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = 10X + 4
σY =
6.Hard
n = 11, p = 0.7: P(X = 4) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 4 correct answers?

n = 11p = 0.7k = 4
P =

Answer key

  1. 1. P = 0.1667
  2. 2. P = 0.05556
  3. 3. P = 0.3056
  4. 4. Var(X) = 2.04
  5. 5. σY = 8.367
  6. 6. P = 0.01733

Full step-by-step solutions: practise this topic on examproblems.com.