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)00.1510.0520.330.1540.35

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

x: 0, 1, 2, 3, 4p(x): 0.15, 0.05, 0.3, 0.15, 0.35
E(X) =
2.Easy
xp(x)00.2520.2540.26?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 6).

x: 0, 2, 4, 6p(x): 0.25, 0.25, 0.2, ?
P(X = 6) =
3.Medium
n = 13k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 13? The order does not matter.

n = 13k = 3
N =
4.Medium
xp(x)00.310.220.1530.35μ = 1.55

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

x: 0, 1, 2, 3p(x): 0.3, 0.2, 0.15, 0.35
σ =
5.Hard
xp(x)00.3520.2540.1560.25μ

X has the distribution shown, and Y = 0.5X + 4. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.35, 0.25, 0.15, 0.25Y = 0.5X + 4
σY =
6.Hard
n = 6, p = 0.3: P(X = 3) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 3 correct answers?

n = 6p = 0.3k = 3
P =

Answer key

  1. 1. E(X) = 2.5
  2. 2. P(X = 6) = 0.3
  3. 3. N = 286
  4. 4. σ = 1.244
  5. 5. σY = 1.187
  6. 6. P = 0.1852

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