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)10.2520.33?40.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 1, 2, 3, 4p(x): 0.25, 0.3, ?, 0.35
P(X = 3) =
2.Easy
xp(x)10.2520.1530.3540.25

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

x: 1, 2, 3, 4p(x): 0.25, 0.15, 0.35, 0.25
E(X) =
3.Medium
xp(x)100.3200.2300.35400.15μ = 23.5

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

x: 10, 20, 30, 40p(x): 0.3, 0.2, 0.35, 0.15
Var(X) =
4.Medium
n = 15k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 15? The order does not matter.

n = 15k = 5
N =
5.Hard
xp(x)00.0510.320.0530.2540.35μ

X has the distribution shown, and Y = 0.5X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.05, 0.3, 0.05, 0.25, 0.35Y = 0.5X + 1
σY =
6.Hard
n = 10, p = 0.5: P(X = 4) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 4 correct answers?

n = 10p = 0.5k = 4
P =

Answer key

  1. 1. P(X = 3) = 0.1
  2. 2. E(X) = 2.6
  3. 3. Var(X) = 112.8
  4. 4. N = 3003
  5. 5. σY = 0.6796
  6. 6. P = 0.2051

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