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)00.051?20.2530.240.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2, 3, 4p(x): 0.05, ?, 0.25, 0.2, 0.35
P(X = 1) =
2.Easy
red: 8blue: 5green: 2

A bag holds 8 red, 5 blue and 2 green balls. You draw one at random. What is the probability P that it is red?

8 / 5 / 2
P =
3.Medium
xp(x)100.2200.1300.35400.35μ = 28.5

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

x: 10, 20, 30, 40p(x): 0.2, 0.1, 0.35, 0.35
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7?8P(six) = 1/6 on each roll

A fair die is rolled 8 times. What is the probability P of getting at least one six?

n = 8
P =
5.Hard
n = 12, p = 0.25: P(X = 5) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 5 correct answers?

n = 12p = 0.25k = 5
P =
6.Hard
n = 7, p = 0.3: P(X = 1) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 1 correct answers?

n = 7p = 0.3k = 1
P =

Answer key

  1. 1. P(X = 1) = 0.15
  2. 2. P = 0.5333
  3. 3. Var(X) = 122.8
  4. 4. P = 0.7674
  5. 5. P = 0.1032
  6. 6. P = 0.2471

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