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)100.2200.330?400.15

The table gives the probability distribution of X, but one probability is missing. Find P(X = 30).

x: 10, 20, 30, 40p(x): 0.2, 0.3, ?, 0.15
P(X = 30) =
2.Easy
xp(x)00.12?40.2560.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 2, 4, 6p(x): 0.1, ?, 0.25, 0.3
P(X = 2) =
3.Medium
xp(x)10.2520.130.3540.3μ = 2.7

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

x: 1, 2, 3, 4p(x): 0.25, 0.1, 0.35, 0.3
Var(X) =
4.Medium
n = 15k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 15? The order does not matter.

n = 15k = 2
N =
5.Hard
€p(x)−50.68200.3450.02

A game costs €5 to play. You win €25 with probability 0.3 and €50 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 = 0.3€50: p = 0.02
E(G) = €
6.Hard
n = 6, p = 0.3: P(X = 3) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 3 correct answers?

n = 6p = 0.3k = 3
P =

Answer key

  1. 1. P(X = 30) = 0.35
  2. 2. P(X = 2) = 0.35
  3. 3. Var(X) = 1.31
  4. 4. N = 105
  5. 5. E(G) = 3.5 €
  6. 6. P = 0.1852

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