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)0?10.3520.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 1, 2p(x): ?, 0.35, 0.35
P(X = 0) =
2.Easy
xp(x)00.310.1520.330.25

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

x: 0, 1, 2, 3p(x): 0.3, 0.15, 0.3, 0.25
E(X) =
3.Medium
n = 12k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 12? The order does not matter.

n = 12k = 2
N =
4.Medium
P(at least one six) = ??1?2?3?4?5?6P(six) = 1/6 on each roll

A fair die is rolled 6 times. What is the probability P of getting at least one six?

n = 6
P =
5.Hard
xp(x)10.320.330.340.1μ

X has the distribution shown, and Y = 10X + 4. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.3, 0.3, 0.3, 0.1Y = 10X + 4
σY =
6.Hard
€p(x)−20.760.25380.05

A game costs €2 to play. You win €8 with probability 0.25 and €40 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€8: p = 0.25€40: p = 0.05
E(G) = €

Answer key

  1. 1. P(X = 0) = 0.3
  2. 2. E(X) = 1.5
  3. 3. N = 66
  4. 4. P = 0.6651
  5. 5. σY = 9.798
  6. 6. E(G) = 2 €

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