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)10.220.33?40.15

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

x: 1, 2, 3, 4p(x): 0.2, 0.3, ?, 0.15
P(X = 3) =
2.Easy
sum = 11die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 11?

2 dice= 11
P =
3.Medium
n = 8k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 8? The order does not matter.

n = 8k = 2
N =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
5.Hard
xp(x)00.3510.3520.3μ

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3Y = 0.5X + 1
σY =
6.Hard
n = 11, p = 0.2: P(X = 3) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 3 correct answers?

n = 11p = 0.2k = 3
P =

Answer key

  1. 1. P(X = 3) = 0.35
  2. 2. P = 0.05556
  3. 3. N = 28
  4. 4. P = 0.7209
  5. 5. σY = 0.4023
  6. 6. P = 0.2215

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