Brain Teasers
Jen's Circus Trip
Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.Probability
Jennifer lives in a rural community and farms with her parents for a living. Most of the time she loves this life and enjoys farming immensely. However, sometimes she really enjoys getting a break from the hard farming life and going somewhere to just have fun. Her favourite place to do this is the circus, and this February they're in town! This February is not on a leap year, and it is unique in that it has four of each day (4 Sundays, 4 Mondays, 4 Tuesdays, etc).
Jen is all excited about the circus, and wants to go very badly. But, she still has chores to do around the farm. Every other Wednesday (the first and third week), she collects the eggs from the chickens and refills their feed bucket. On Sundays, she and her entire family go to church, as they are very religious. On the second week of the month, many of their sheep are due to have lambs, so she has to stay home and help. Fridays are taken up by grooming the horses and cows.
If she puts her savings together, she will be able to afford one regular price ticket. But then she will have no money left for candy floss. Luckily, the circus has a special on: on 5 random days of the month, they will have a discount for farmers only. This discount will allow Jen to buy a ticket as well as lots of candy floss. There's only one catch. They only announce that the special will be on the day before. There would be no planning ahead for it. This makes Jen feel blue, and she thinks that she probably won't make it on any of the discount days.
Question:
What is the probability of Jen being able to go on a discount day?
Jen is all excited about the circus, and wants to go very badly. But, she still has chores to do around the farm. Every other Wednesday (the first and third week), she collects the eggs from the chickens and refills their feed bucket. On Sundays, she and her entire family go to church, as they are very religious. On the second week of the month, many of their sheep are due to have lambs, so she has to stay home and help. Fridays are taken up by grooming the horses and cows.
If she puts her savings together, she will be able to afford one regular price ticket. But then she will have no money left for candy floss. Luckily, the circus has a special on: on 5 random days of the month, they will have a discount for farmers only. This discount will allow Jen to buy a ticket as well as lots of candy floss. There's only one catch. They only announce that the special will be on the day before. There would be no planning ahead for it. This makes Jen feel blue, and she thinks that she probably won't make it on any of the discount days.
Question:
What is the probability of Jen being able to go on a discount day?
Hint
The number of days that Jen is busy can be simplified into one number.Answer
15 days out of 28 Jen is busy (2 Wednesdays, 4 Fridays, 4 Sundays, and 1 week for sheep, less Sunday & Friday). The chance of Jen missing one of the discount days is 15/28 or 53.57%. The chances of Jen missing the second discount day is 14/27 or 51.85%, the 3rd 13/26 (50%), the 4th 12/25 (48%), the 5th 11/24 (45.83). The chance of her missing all 5 would be 53.57%x51.85%x50%x48%x43.83% or ((15*14*13*12*11)/(28*27*26*25*24)) = 3%.Therefore, the probability that Jen is able to go on a discount day is about 97% (96.94% actually).
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Comments
How is this a rebus?!
Either somebody fixed it or you're looking in the wrong section, Witness.
When I submitted it, I'm pretty sure I put it in the "Probability" category... who knows though. It might have accidentally gotten mixed up...
pish posh booooring
Good teaser. I came close, with 95.59%, but I messed up on the fractions.
I GOT IT
Uh.......That was pretty Booooring.
umm...yeah
Yeah, sorry...I have to agree. It's kinda like a math lesson...too hard to enjoy, I think. Anyway, it's a good math lesson
i was way off i got like 5/58....ok ...whats the probability that anyone knows how i got that answer?
i realized she was going to miss 3 wednesdays altogether 4 fridays.... 4 sundays...and one of everyother day..but the methods on figuring everything else out i got lost. felt like untieng a giant knotted ball of yarn.... but i mean that in a good way
i realized she was going to miss 3 wednesdays altogether 4 fridays.... 4 sundays...and one of everyother day..but the methods on figuring everything else out i got lost. felt like untieng a giant knotted ball of yarn.... but i mean that in a good way
interesting
I oversimplified this one! I thought I was trying to calculate the chance of Jen randomly showing up on a discount day. You did state the question clearly on the last line, but the part about "not being able to plan ahead" made me think she was just going to take her chances. Well I had fun with it the second time I took a stab at it!
very good
i got 2.2% in my 5 min. cal. but i fig. 17 days that left 11 than the 5 bounus days taking her chances like Becka said
I got it!!!
Pretty straight forward math problem.
The solution is more easily stated by saying the chance of missing the five dicount days is the 15C5 (15 choose 5) = 3003 ways of the five discount days occuring on days when Jen is busy divided by the 28C5 = 98280 ways of choosing five discount days in February. This gives the exact probability of 3003/98280 = 1001/32760 = 3.0555...%.
Thus Jen's chances of going are 31759/32760 = 96.9444...%.
The solution is more easily stated by saying the chance of missing the five dicount days is the 15C5 (15 choose 5) = 3003 ways of the five discount days occuring on days when Jen is busy divided by the 28C5 = 98280 ways of choosing five discount days in February. This gives the exact probability of 3003/98280 = 1001/32760 = 3.0555...%.
Thus Jen's chances of going are 31759/32760 = 96.9444...%.
OK, it did not do my confidence much good to read this was "pretty straightforward".
But I did like the puzzle; I always enjoy the ones with a well-written story.
But I did like the puzzle; I always enjoy the ones with a well-written story.
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