anonymous
  • anonymous
In a lottery there are 24 prizes allocated at random to 24 prize-winners. 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
Mathematics
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

KingGeorge
  • KingGeorge
\[{4 \over 24} \times {20 \over 24} \]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.
anonymous
  • anonymous
But the answer should be 11/138.
KingGeorge
  • KingGeorge
11/138? Give me second.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

KingGeorge
  • KingGeorge
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.
KingGeorge
  • KingGeorge
This solution does indeed give you \[11 \over 138\]
anonymous
  • anonymous
Thanks a lot! Can you work out ben's probability using the addition rule?
KingGeorge
  • KingGeorge
What are you using as the addition rule?
anonymous
  • anonymous
For ben: P(Car) + P(Bicycle) - P(Bicycle and car)
KingGeorge
  • KingGeorge
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)=\({3 \over 23}+{8 \over 23}={11 \over 23}\)
KingGeorge
  • KingGeorge
This works because Ben only gets one prize. If he were to get more than one prize, this wouldn't work.
anonymous
  • anonymous
The addition rule is: P(A U B) = P(A) + P(B) - P(A and B).
anonymous
  • anonymous
So how come you don't need to subtract P(A and B)?
KingGeorge
  • KingGeorge
In this case P(A and B)=0 since he can only get one prize.
anonymous
  • anonymous
Oh I see! Thanks!
KingGeorge
  • KingGeorge
you're welcome.

Looking for something else?

Not the answer you are looking for? Search for more explanations.