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: 2blue: 6green: 2

A bag holds 2 red, 6 blue and 2 green balls. You draw one at random. What is the probability P that it is blue?

2 / 6 / 2
P =
2.Easy
xp(x)00.3510.2520.230.14?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 0, 1, 2, 3, 4p(x): 0.35, 0.25, 0.2, 0.1, ?
P(X = 4) =
3.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
Var(X) =
4.Medium
xp(x)00.210.0520.2530.1540.35μ = 2.4

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

x: 0, 1, 2, 3, 4p(x): 0.2, 0.05, 0.25, 0.15, 0.35
σ =
5.Hard
n = 12, p = 0.25: P(X = 5) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 5 correct answers?

n = 12p = 0.25k = 5
P =
6.Hard
n = 9, p = 0.5: P(X = 2) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 2 correct answers?

n = 9p = 0.5k = 2
P =

Answer key

  1. 1. P = 0.6
  2. 2. P(X = 4) = 0.1
  3. 3. Var(X) = 0.7
  4. 4. σ = 1.497
  5. 5. P = 0.1032
  6. 6. P = 0.07031

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