Question

In a lottery there are 100 tickets, of which five have a prize. Indicate the probability that if you buy five tickets, two will have a prize.

Answer 1

There are 100 lottery tickets, of which 5 have a prize. Now 5 tickets are drawn randomly from these 100 tickets.

Any 5 tickets from 100 tickets can be drawn in ¹⁰⁰C₅ =75287520 possible ways.

Now there are 5 tickets having a prize and 95 tickets that do not have any prize. Thus, 2 tickets from these 5 winning tickets can be drawn in ⁵C₂ possible ways and for each way the other (5-2) =3 tickets from the 95 tickets can be drawn in ⁹⁵C₃ possible ways.

Thus, there are ⁵C₂*⁹⁵C₃ possible ways in which 2 prize winning tickets can be drawn from 100 tickets.

Thus, the probability that 2 tickets will have a prize is,

(⁵C₂*⁹⁵C₃)/¹⁰⁰C₅=0.0184(approximately) .

Thus, the required probability is 0.0184.