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: 8green: 4

A bag holds 2 red, 8 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

2 / 8 / 4
P =
2.Easy
red: 3blue: 3green: 1

A bag holds 3 red, 3 blue and 1 green balls. You draw one at random. What is the probability P that it is red?

3 / 3 / 1
P =
3.Medium
xp(x)10.0520.3530.340.3μ = 2.85

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

x: 1, 2, 3, 4p(x): 0.05, 0.35, 0.3, 0.3
σ =
4.Medium
xp(x)100.2200.1300.35400.35μ = 28.5

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

x: 10, 20, 30, 40p(x): 0.2, 0.1, 0.35, 0.35
Var(X) =
5.Hard
xp(x)10.2520.1530.3540.150.15μ

X has the distribution shown, and Y = 2X + 10. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.25, 0.15, 0.35, 0.1, 0.15Y = 2X + 10
σY =
6.Hard
n = 12, p = 0.5: P(X = 3) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 3 correct answers?

n = 12p = 0.5k = 3
P =

Answer key

  1. 1. P = 0.5714
  2. 2. P = 0.4286
  3. 3. σ = 0.9097
  4. 4. Var(X) = 122.8
  5. 5. σY = 2.674
  6. 6. P = 0.05371

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