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)100.3200.35300.340?

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

x: 10, 20, 30, 40p(x): 0.3, 0.35, 0.3, ?
P(X = 40) =
2.Easy
xp(x)100.2200.25300.35400.2

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

x: 10, 20, 30, 40p(x): 0.2, 0.25, 0.35, 0.2
E(X) =
3.Medium
red: 5blue: 7

A bag holds 5 red and 7 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

5 / 7
P =
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
xp(x)10.120.230.3540.35μ

X has the distribution shown, and Y = −2X + 4. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.1, 0.2, 0.35, 0.35Y = −2X + 4
σY =
6.Hard
xp(x)00.210.220.2530.35μ

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

x: 0, 1, 2, 3p(x): 0.2, 0.2, 0.25, 0.35Y = 2X + 5
σY =

Answer key

  1. 1. P(X = 40) = 0.05
  2. 2. E(X) = 25.5
  3. 3. P = 0.1515
  4. 4. P = 0.7674
  5. 5. σY = 1.947
  6. 6. σY = 2.269

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