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)100.15200.2300.3540?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 40).

x: 10, 20, 30, 40p(x): 0.15, 0.2, 0.35, ?
P(X = 40) =
2.Easy
xp(x)00.3510.320.35

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
E(X) =
3.Medium
n = 8k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 8? The order does not matter.

n = 8k = 4
N =
4.Medium
n = 11k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 11? The order does not matter.

n = 11k = 5
N =
5.Hard
xp(x)00.3510.3520.3μ

X has the distribution shown, and Y = 2X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.35, 0.3Y = 2X + 5
σY =
6.Hard
n = 6, p = 0.4: P(X = 5) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.4, independently. What is the probability P of exactly 5 correct answers?

n = 6p = 0.4k = 5
P =

Answer key

  1. 1. P(X = 40) = 0.3
  2. 2. E(X) = 1
  3. 3. N = 70
  4. 4. N = 462
  5. 5. σY = 1.609
  6. 6. P = 0.03686

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