Question

For an instant lottery, it is known that 10% of tickets will win an amount of money. a) What is the expected number of tickets that must be bought in order to find a winning ticket? Answer b) What is the probability that more than 10 tickets must be bought in order to find a winning ticket? {3 decimal places) Answer c) Find the probability that exactly 20 tickets must be purchased to find two winning tickets? {4 decimal places)

Answer 1

a)

let x denote number of tickets purchased

then X~geo(p=0.10)

10% of tickets will win an amount of money.

so, expected number of tickets that must be bought in order to find a winning ticket =1/p = 10

b)

more than 10 tickets must be bought in order to find a winning ticket

it means upto 10 tickets there is no winning price

so, P(no winning ticket upto 10 tickets) = (1-0.10)^10 =0.3487

so, P(more than 10 tickets must be bought in order to find a winning ticket) = 1 - 0.3487 =0.6513

c)

P(exactly 20 tickets must be purchased to find two winning tickets) = (1-0.10)^18 *0.10² = 0.0015