SOLUTION: There are ten lottery tickets, two of which are winners. Find the probability that in a sample of 6 tickets there will be no more than one winning ticket.

Question 370130: There are ten lottery tickets, two of which are winners. Find the probability that in a sample of 6 tickets there will be no more than one winning ticket.

Found 2 solutions by edjones, spacesurfer:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
nCr=combinayion of n things taken r at a time.
((8C5 * 2C1)+(8C6))/10C6
=((56*2)+28)/210
=2/3 the probability that in a sample of 6 tickets there will be no more than one winning ticket.
.
Ed
Answer by spacesurfer(12) (Show Source): You can put this solution on YOUR website!
First, there are a total of 210 ways to choose 6 tickets out of 10. That's 10 choose 6 = 210.
If there are 0 winners, then there are 8 tickets to choose from that are not winners (that's 10 total tickets - 2 winning tickets = 8 non-winners). So that means 8 choose 6 = 28 ways you can choose 6 tickets from 8 non-winning tickets where 0 are winners.
If there is 1 winner, then there you have 5 left for a non-winner. Hence, 8 choose 5 = 56. But there are 2 winners to choose from, so that's 2 x 56 = 112 ways 1 is a winner that 5 non-winners. Think of this this way: 2 winners to choose from x 56 ways to choose 5 out of 8 non-winners. Hence, it's 2 x (8 choose 5) - 112.
Add up 0 winners or 1 winner and you get 28 + 112 = 140.
Total possibilities = 210. So 140/210 = 2/3.
RELATED QUESTIONS
There are ten lottery tickets, two of which are winners. Find the probability that in a... (answered by edjones)
There are ten raffle tickets, two of which are winners. Find the probability that in a... (answered by jvan,spacesurfer)
Thre are twelve raffle tickets, three of which are winners. Find the probability that in... (answered by ewatrrr)
there are 60 tickets sold. 30 winners will be chosen. You have three tickets. What is... (answered by stanbon)
Info: There are two little lotteries in town, each of which sells exactly 100 tickets. (answered by sudhanshu_kmr)
For #1 - #6 suppose there are two little lotteries in town, each of which sells exactly... (answered by ikleyn)
(Info needed to solve the question, There are two little lotteries in town, each of which (answered by rfer)
Molly and Ming each purchase one raffle ticket. If a total of ten raffle tickets are... (answered by ikleyn)
Suppose there are two raffles. In each raffle there are 100 tickets, 10 of which are... (answered by stanbon)