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
xp(x)00.2510.1520.253?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 0, 1, 2, 3p(x): 0.25, 0.15, 0.25, ?
P(X = 3) =
2.Easy
xp(x)1?20.2530.2540.2

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 1, 2, 3, 4p(x): ?, 0.25, 0.25, 0.2
P(X = 1) =
3.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 =
4.Medium
xp(x)00.210.1520.3530.0540.25μ = 2

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

x: 0, 1, 2, 3, 4p(x): 0.2, 0.15, 0.35, 0.05, 0.25
σ =
5.Hard
xp(x)00.3520.240.160.35μ

X has the distribution shown, and Y = 0.5X + 10. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.35, 0.2, 0.1, 0.35Y = 0.5X + 10
σY =
6.Hard
n = 7, p = 0.5: P(X = 1) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 1 correct answers?

n = 7p = 0.5k = 1
P =

Answer key

  1. 1. P(X = 3) = 0.35
  2. 2. P(X = 1) = 0.3
  3. 3. P = 0.4213
  4. 4. σ = 1.414
  5. 5. σY = 1.284
  6. 6. P = 0.05469

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