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)100.3200.1300.25400.35

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

x: 10, 20, 30, 40p(x): 0.3, 0.1, 0.25, 0.35
E(X) =
2.Easy
red: 4blue: 2

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

4 / 2
P =
3.Medium
xp(x)00.3510.1520.2530.25μ = 1.4

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

x: 0, 1, 2, 3p(x): 0.35, 0.15, 0.25, 0.25
Var(X) =
4.Medium
xp(x)100.35200.3300.15400.2μ = 22

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

x: 10, 20, 30, 40p(x): 0.35, 0.3, 0.15, 0.2
σ =
5.Hard
n = 7, p = 0.2: P(X = 5) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 5 correct answers?

n = 7p = 0.2k = 5
P =
6.Hard
n = 5, p = 0.25: P(X = 2) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 2 correct answers?

n = 5p = 0.25k = 2
P =

Answer key

  1. 1. E(X) = 26.5
  2. 2. P = 0.6667
  3. 3. Var(X) = 1.44
  4. 4. σ = 11.22
  5. 5. P = 0.004301
  6. 6. P = 0.2637

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