Question 1135024: Suppose a local food bank is selling raffle tickets as a fundraiser and claims that each raffle ticket has a 3% chance of winning one of several prizes. Additionally, suppose an animal shelter is also selling raffle tickets for a different fundraiser, and reveals that there are 1200 total tickets, and exactly 48 will win a prize.
1. If you bought 150 raffle tickets for the animal shelter’s fundraiser, how many tickets would you expect to be winners?
2. If you bought 150 raffle tickets for the food bank’s fundraiser, how many tickets would you expect to be winners?
3. If you bought 150 tickets for each raffle, is it possible that none of the tickets will win? Explain your answer.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! for the food bank, the probability of winning one of several prizes is 3%.
for the animal shelter, the probability of one of several prizes is 48 / 1200 which is 4%.
for number 1, 4% of 150 = .04 * 150 = 6 winning tickets.
you can expect about 6 winning tickets for every 150 tickets bought on the average.
for number 2, 3% of 150 = .03 * 150 = 4.5 winning tickets.
you can expect about 4.5 winning tickets for every 150 tickets bought on the average.
what you actually win can be more or less than those average figures.
for number 3, yes it is possible that none of the tickets will win.
how to explain?
the average expectation is just that.
it's an average.
each set of tickets bought can have more or less than the average expected, but when you add up all the sets of tickets bought, the overall average will be 3% for the food bank and 4% for the animal shelter.
an example:
animal shelter sells 1200 tickets.
assuming everybody buys 150 tickets each, then there are 8 sets of 150 tickets purchased.
it is possible that a number of those sets contains no winners and the average number of winners for each set will still be 6.
since the total number of winners has to be 48, then if some sets have fewer than 6 winners, other sets must have more than 6 winners in order for the average to hold true.
a possible scenario would be set 1 = 0 winners, set 2 = 0 winners, set 3 = 0 winners, set 4 = 20 winners, set 5 = 10 winners, set 6 = 5 winners, set 7 = 2 winners, set 8 = 11 winners.
there's a total of 48 winners.
the average number of winners for each set is 48/8 = 6, but none of the sets has exactly 6 winners.
however, the average for each set is still 6 because the average is determined by dividing the total number of possible winners by the number of sets, which in this case is 48/8 = 6.
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