Question

The probability that Paul wins a raffle is given by the expression n/n+6. Write down an expression, in the form of a combined single fraction, for the probability that Paul does not win.

Answer 1

`P(W') = (6)/(n+6)`

Explanation:

Let P(W) represents the probability that Paul wins

Let P(W') represents the probability that Paul does not win

Given

`P(W) = (n)/(n+6)`

Required

`P(W')`

In probability, the sum of opposite probability equals 1;

This implies that

`P(W) + P(W') = 1`

Substitute
`P(W) = (n)/(n+6)` in the above equation

`P(W) + P(W') = 1` becomes

`(n)/(n+6)+ P(W') = 1`

Subtract
`(n)/(n+6)` from both sides

`(n)/(n+6) - (n)/(n+6) + P(W') = 1 - (n)/(n+6)`

`P(W') = 1 - (n)/(n+6)`

Solve fraction (start by taking the LCM)

`P(W') = (n + 6 - n)/(n+6)`

`P(W') = (n - n + 6)/(n+6)`

`P(W') = (6)/(n+6)`

Hence, the probability that Paul doesn't win is
`P(W') = (6)/(n+6)`