Question

In a raffle, the winners of the first and second prizes each receive one ticket to an upcoming concert. You and a friend each buy a raffle ticket along with 12 other people. What is the exact probability that you win the first prize and your friend wins the second prize?

Answer 1

There are a total of 14 tickets in the raffle, and two of them will be selected as the winners of the first and second prizes.

The probability that you win the first prize is 1/14, since there is only one winning ticket out of 14 tickets. After your ticket is drawn as the winner of the first prize, there are only 13 tickets left, one of which is your friend's ticket.

The probability that your friend wins the second prize, given that you have already won the first prize, is 1/13, since there is only one winning ticket left out of the 13 remaining tickets.

Therefore, the exact probability that you win the first prize and your friend wins the second prize is:

(1/14) * (1/13) = 1/182

So the probability is 1 out of 182, or approximately 0.0055, or 0.55%

Explanation:

Answer 2

`\sf Probability=(1)/(182)`

Explanation:

Given you and a friend each buy a raffle ticket along with 12 other people:

• Total number of raffle tickets sold = 14

`\boxed{\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)}`

The first prize is the first raffle ticket drawn. Therefore, the probability of winning the first prize is:

`\sf \bullet \quad P(first\;prize)=(1)/(14)`

After the first raffle ticket is drawn, there are a total of 13 raffle tickets remaining.

The second prize is the next raffle ticket drawn. Therefore, the probability of winning the second prize is:

`\sf \bullet \quad P(first\;prize)=(1)/(13)`

To calculate the exact probability that you win the first prize and your friend wins the second prize, multiply the found probabilities:

`\implies \sf Probability=(1)/(14)*(1)/(13)`

`\implies \sf Probability=(1)/(182)`

Therefore, the exact probability that you win the first prize and your friend wins the second prize is:

`\bullet \quad \sf (1)/(182)`