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)00.31?20.35

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

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

Two fair dice are rolled. What is the probability P that the sum is exactly 4?

2 dice= 4
P =
3.Medium
red: 3blue: 9

A bag holds 3 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 9
P =
4.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 =
5.Hard
n = 6, p = 0.3: P(X = 1) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 1 correct answers?

n = 6p = 0.3k = 1
P =
6.Hard
n = 11, p = 0.25: P(X ≤ 1) = ?k01234567891011

11 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 11p = 0.25
P =

Answer key

  1. 1. P(X = 1) = 0.35
  2. 2. P = 0.08333
  3. 3. P = 0.04545
  4. 4. P = 0.3056
  5. 5. P = 0.3025
  6. 6. P = 0.1971

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