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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Name: ____________________   Date: ____________

1.Easy
red: 3blue: 6green: 5

A bag holds 3 red, 6 blue and 5 green balls. You draw one at random. What is the probability P that it is blue?

3 / 6 / 5
P =
2.Easy
xp(x)00.3510.1520.13?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): 0.35, 0.15, 0.1, ?, 0.2
P(X = 3) =
3.Medium
xp(x)00.310.3520.330.05μ = 1.1

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

x: 0, 1, 2, 3p(x): 0.3, 0.35, 0.3, 0.05
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7?8P(six) = 1/6 on each roll

A fair die is rolled 8 times. What is the probability P of getting at least one six?

n = 8
P =
5.Hard
n = 6, p = 0.25: P(X = 4) = ?k0123456

A test has 6 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 = 6p = 0.25k = 4
P =
6.Hard
n = 6, p = 0.6: P(X = 5) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 5 correct answers?

n = 6p = 0.6k = 5
P =

Answer key

  1. 1. P = 0.4286
  2. 2. P(X = 3) = 0.2
  3. 3. Var(X) = 0.79
  4. 4. P = 0.7674
  5. 5. P = 0.03296
  6. 6. P = 0.1866

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