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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Name: ____________________   Date: ____________

1.Easy
xp(x)100.25200.35300.0540?

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

x: 10, 20, 30, 40p(x): 0.25, 0.35, 0.05, ?
P(X = 40) =
2.Easy
xp(x)0?20.140.3560.2

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

x: 0, 2, 4, 6p(x): ?, 0.1, 0.35, 0.2
P(X = 0) =
3.Medium
n = 9k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 9? The order does not matter.

n = 9k = 2
N =
4.Medium
xp(x)10.3520.0530.240.150.3μ = 2.95

For the distribution shown, find the standard deviation σ of X.

x: 1, 2, 3, 4, 5p(x): 0.35, 0.05, 0.2, 0.1, 0.3
σ =
5.Hard
xp(x)00.2520.1540.3560.25μ

X has the distribution shown, and Y = −2X + 10. Find the standard deviation σY of Y.

x: 0, 2, 4, 6p(x): 0.25, 0.15, 0.35, 0.25Y = −2X + 10
σY =
6.Hard
€p(x)−50.88200.12450.02

A game costs €5 to play. You win €25 with probability 0.1 and €250 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€25: p = 0.1€250: p = 0.02
E(G) = €

Answer key

  1. 1. P(X = 40) = 0.35
  2. 2. P(X = 0) = 0.35
  3. 3. N = 36
  4. 4. σ = 1.658
  5. 5. σY = 4.454
  6. 6. E(G) = 2.5 €

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