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)00.110.1520.253?40.2

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

x: 0, 1, 2, 3, 4p(x): 0.1, 0.15, 0.25, ?, 0.2
P(X = 3) =
2.Easy
sum ≥ 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 5?

2 dice≥ 5
P =
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)10.3520.130.2540.3μ = 2.5

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

x: 1, 2, 3, 4p(x): 0.35, 0.1, 0.25, 0.3
σ =
5.Hard
n = 9, p = 0.7: P(X ≤ 1) = ?k0123456789

9 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 9p = 0.7
P =
6.Hard
n = 7, p = 0.25: P(X = 4) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 4 correct answers?

n = 7p = 0.25k = 4
P =

Answer key

  1. 1. P(X = 3) = 0.3
  2. 2. P = 0.8333
  3. 3. P = 0.4213
  4. 4. σ = 1.245
  5. 5. P = 0.000433
  6. 6. P = 0.05768

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