Probability
posted by William .
In a raffle there are four winning tickets from 12, What is the probability from six tickets there are two winners?
Thank you in advance.

The number of getting two winning tickets out of six is 6! / (2! x 4!) = 6x5/2 = 15.
Consider the probability of getting one of those 15 outcomes  say just the first two are winners, and the final four are losers. The chances of that happening  remember you're choosing WITHOUT replacement, so the odds of picking a winning ticket change every time  are (4/12) x (3/11) x (8/10) x (7/9) x (6/8) x (5/7) = (1/33).
Now consider the probability of getting a different combination of winners and losers in which there are still just two winners  say the 2nd and 4th one are the winners. The odds of THAT happening are (8/12) x (4/11) x (7/10) x (3/9) x (6/8) x (5/7). The denominators are exactly the same as before, and the numerators have just all been shuffled around  so the product of them all is the same as before, namely (1/33).
Try any other combination, and you'll see that exactly the same thing happens again. So the answer should be the total number of ways of getting two winners out of six times the probability of any one of them happening, namely 15 x (1/33). So I reckon the answer is (15/33).
Respond to this Question
Similar Questions

Statistics
"A batch of 350 raffle tickets contains three winning tickets. You buy five tickets. What is the probability that you have (a) no winning tickets, (b) all of the winning tickets, (c) at least one winning ticket, and (d) at least one … 
probability
A batch of 350 raffle tickets contains 4 winning tickets. You buy 4 tickets. What is the probability you have no winning tickets? 
probability
A batch of 350 raffle tickets contatins 4 winning tickets. You buy 4 tickets. What is the probability that you have: a.) No winning tickets? 
Probability
A school is running a raffle for two prizes. 59 tickets were sold for the raffle, numbered 1,…,59. All the tickets are put into a hat and a teacher picks out two tickets which have numbers i and j from the hat. What is the expected … 
Math
I have 5 tickets for a raffle and I know that the probability of my winning the prize is 0.003. How many tickets were sold altogether? 
Statistics
A school is running a raffle. There are 100 tickets, of which 3 are winners. You can assume that tickets are sold by drawing at random without replacement from the available tickets. Teacher X buys 10 raffle tickets, and so does Teacher … 
Statistic
a batch of 350 raffle tickets contains four winning tickets. you buy four tickets. what is the probability that you have at least one winning ticket? 
Math
the probability of having a winning raffle ticket is 15%. If you bought 40 tickets, how many winning tickets should you expect to have? 
math
A raffle contains 200 tickets, two of this 200 tickets are the 1st and 2nd price, if i were to buy 5 tickets, what is my probability of winning 1st price? 
Math Probability
The probability of having a winning raffle ticket is 20%. If you bought 50 tickets, how many wining tickets should you expect to have?