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

Answer:

$P(W') = \frac{6}{n+6}$

Step-by-step explanation:

Let P(W) represents the probability that Paul wins

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

Given

$P(W) = \frac{n}{n+6}$

Required

$P(W')$

In probability, the sum of opposite probability equals 1;

This implies that

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

Substitute $P(W) = \frac{n}{n+6}$ in the above equation

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

$\frac{n}{n+6}+ P(W') = 1$

Subtract $\frac{n}{n+6}$ from both sides

$\frac{n}{n+6} - \frac{n}{n+6} + P(W') = 1 - \frac{n}{n+6}$

$P(W') = 1 - \frac{n}{n+6}$

Solve fraction (start by taking the LCM)

$P(W') = \frac{n + 6 - n}{n+6}$

$P(W') = \frac{n - n + 6}{n+6}$

$P(W') = \frac{6}{n+6}$

Hence, the probability that Paul doesn't win is $P(W') = \frac{6}{n+6}$