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)1?20.1530.1540.35

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

x: 1, 2, 3, 4p(x): ?, 0.15, 0.15, 0.35
P(X = 1) =
2.Easy
red: 8blue: 5green: 5

A bag holds 8 red, 5 blue and 5 green balls. You draw one at random. What is the probability P that it is blue?

8 / 5 / 5
P =
3.Medium
xp(x)00.3510.3520.0530.140.15μ = 1.35

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.35, 0.05, 0.1, 0.15
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5?6P(six) = 1/6 on each roll

A fair die is rolled 6 times. What is the probability P of getting at least one six?

n = 6
P =
5.Hard
n = 12, p = 0.7: P(X = 4) = ?k0123456789101112

A test has 12 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 = 12p = 0.7k = 4
P =
6.Hard
n = 6, p = 0.4: P(X = 2) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 2 correct answers?

n = 6p = 0.4k = 2
P =

Answer key

  1. 1. P(X = 1) = 0.35
  2. 2. P = 0.2778
  3. 3. Var(X) = 2.027
  4. 4. P = 0.6651
  5. 5. P = 0.007798
  6. 6. P = 0.311

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