Probability

Question

There is a 17% probability that Shirley will eat steak for her birthday, and there is a 20% chance that she will eat cake.  If there is a 10% chance that she will eat steak or cake, what is the likelihood that she will pig out and eat both?

Answer 1

I'm choking on this one...

 

It seems to me that the probability of doing A OR B can't be less than the probability of doing just one.

 

Also, the probability of A and B is (I thought) the product of the independent probabilities

 

Putting that aside, the rule is:

p(A OR B) = p(A) + p(B) -p (A AND B)

 

Until someone jumps in with the answer, tell us what's in your notes that might shed some light.

 

 

Answer 2

One formula for relating the probability of an AND to an (exclusive) OR is:

 

P(A or B) = P(A) + P(B) - P(A and B)

 

This assumes that the OR is exclusive, which is implied in that it is only 10%. Otherwise it would be much higher.

 

Given the information in the problem, you can easily solve this formula.

 

10% = 17% + 20% - P(A and B)

 

P(A and B) = 17% + 20% - 10% = 27%

 

Make sense?