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)00.310.3520.35

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
E(X) =
2.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 red?

2 / 6 / 2
P =
3.Medium
n = 6k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 6? The order does not matter.

n = 6k = 3
N =
4.Medium
red: 3blue: 4

A bag holds 3 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 4
P =
5.Hard
xp(x)00.320.2540.3560.1μ

X has the distribution shown, and Y = 3X + 4. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.3, 0.25, 0.35, 0.1Y = 3X + 4
σY =
6.Hard
n = 7, p = 0.4: P(X = 3) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 3 correct answers?

n = 7p = 0.4k = 3
P =

Answer key

  1. 1. E(X) = 1.05
  2. 2. P = 0.2
  3. 3. N = 20
  4. 4. P = 0.1429
  5. 5. σY = 5.962
  6. 6. P = 0.2903

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