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adnanchowdhury
Group Title
In a lottery there are 24 prizes allocated at random to 24 prizewinners. Ann, Ben, and Cal are three of the winners. Of the prizes, 4 are cars, 8 are bicycles and 12 are watches.
Find the probability that Ann gets a car and Ben gets a car or bicycle
 2 years ago
 2 years ago
adnanchowdhury Group Title
In a lottery there are 24 prizes allocated at random to 24 prizewinners. Ann, Ben, and Cal are three of the winners. Of the prizes, 4 are cars, 8 are bicycles and 12 are watches. Find the probability that Ann gets a car and Ben gets a car or bicycle
 2 years ago
 2 years ago

This Question is Closed

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
\[{4 \over 24} \times {20 \over 24} \]The 4/24 is Ann's chance of getting a car, and the 20/24 is Ben's chance of getting a car or a bike.
 2 years ago

adnanchowdhury Group TitleBest ResponseYou've already chosen the best response.0
But the answer should be 11/138.
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
11/138? Give me second.
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
My bad, I was calculating the probability that Ben got a bike or a watch, not a bike or a car. In this case, the probability is given by \[{4 \over 24} \times {{3+8} \over 23}\]Where 4/24 is the probability that Ann gets a car, and the other term is the chance Ben got a car plus the chance he got a bike.
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
This solution does indeed give you \[11 \over 138\]
 2 years ago

adnanchowdhury Group TitleBest ResponseYou've already chosen the best response.0
Thanks a lot! Can you work out ben's probability using the addition rule?
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
What are you using as the addition rule?
 2 years ago

adnanchowdhury Group TitleBest ResponseYou've already chosen the best response.0
For ben: P(Car) + P(Bicycle)  P(Bicycle and car)
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
nm, I realized I knew it. By the addition rule, Ben's probability is P(Car)=\(3 \over 23\) and P(Bike) =\(8 \over 23\) so P(Car)+P(Bike)=P(Car or Bike)=\({3 \over 23}+{8 \over 23}={11 \over 23}\)
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
This works because Ben only gets one prize. If he were to get more than one prize, this wouldn't work.
 2 years ago

adnanchowdhury Group TitleBest ResponseYou've already chosen the best response.0
The addition rule is: P(A U B) = P(A) + P(B)  P(A and B).
 2 years ago

adnanchowdhury Group TitleBest ResponseYou've already chosen the best response.0
So how come you don't need to subtract P(A and B)?
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
In this case P(A and B)=0 since he can only get one prize.
 2 years ago

adnanchowdhury Group TitleBest ResponseYou've already chosen the best response.0
Oh I see! Thanks!
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
you're welcome.
 2 years ago
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