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: 2green: 1

A bag holds 3 red, 2 blue and 1 green balls. You draw one at random. What is the probability P that it is blue?

3 / 2 / 1
P =
2.Easy
xp(x)10.3520.130.240.35

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 1, 2, 3, 4p(x): 0.35, 0.1, 0.2, 0.35
E(X) =
3.Medium
xp(x)00.2510.3520.230.2μ = 1.35

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

x: 0, 1, 2, 3p(x): 0.25, 0.35, 0.2, 0.2
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
5.Hard
xp(x)00.210.320.130.3540.05μ

X has the distribution shown, and Y = 0.5X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.2, 0.3, 0.1, 0.35, 0.05Y = 0.5X + 10
σY =
6.Hard
n = 12, p = 0.6: P(X = 1) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 1 correct answers?

n = 12p = 0.6k = 1
P =

Answer key

  1. 1. P = 0.3333
  2. 2. E(X) = 2.55
  3. 3. Var(X) = 1.127
  4. 4. P = 0.5177
  5. 5. σY = 0.63
  6. 6. P = 0.000302

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