Question

Tickets for an upcoming concert are sold out but a local charity is having a raffle and the prize is a pair of tickets to the concert. One hundred people enter the raffle, so each individual who entered has 1/100 probability of winning the pair of tickets. You and a friend both entered. What is the probability that one or the other of you wins the tickets

Answer 1

`P(A\ or\ B) = (1)/(50)`

Explanation:

Represent the event that you win with A and the even that your friend win with B.

So, we have:

`P(A) = (1)/(100)`

`P(B) = (1)/(100)`

Required

Calculate P(A or B)

Both events are mutually exclusive.

So:

`P(A\ or\ B) = P(A) + P(B)`

Substitute values for P(A) and P(B)

`P(A\ or\ B) = (1)/(100) + (1)/(100)`

Take LCM

`P(A\ or\ B) = (1+1)/(100)`

`P(A\ or\ B) = (2)/(100)`

Simplify:

`P(A\ or\ B) = (1)/(50)`