I was wondering if I got this question right.

A food distributor carries 64 varieties of salad dressing. Appleton Markets stocks 48 of these flavors. Beacon Stores carries 32 of them. The probability that a flavor will be carried by Appleton or Beacon is 15/16. Find the probability a flavor is carried by both Appleton and Beacon.


I thought the answer would be 3/8, am I wrong?

VERY INTERESTING!

Obviously, A carries 48, B carries 32

AND (! ) A and B togather carry = 15/16 times 64 = 60

Hence B carries (60 - 48) = 12 that are NOT carried by A

Hence B carries (32 -12) = 20 that are also carried by A
\
Carried by BOTH = 20

Hence probability = 20/64 = 5/16

Please confirm if correct or not.

FORMAL METHOD;

Remember:

P (C1 U C2) = P(C1) + P(C2) - P(C1 intersection C2)

and P (C1) = 48/64, P(C2) = 32/64, P(C1 U C2) = 15/16

HENCE P(C1 intersection C2) = 5/16

EDIT: I re-read the problem and the line:

AND (!!) A and B togather carry = 15/16 times 64 = 60

Could that mean the same as OR (3rd sentence)?

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I was close to being right :cool: . 3/8 or 6/16 was really close to your 5/16. Thanks for both the formal and informal method of solving probabilities. I understand how you arrived at the answer.

PS: I understood the informal method better.

Thanks again.:D

It means that stores A and B (either or both) carry...

For example: A carries X and Y

B carries Y and Z

A and B together carry X, Y and Z

Thanks again for being helpful.:D :cool: