Question

Consider this word problem about baking cookies:You are baking cookies for your class. You put pink frosting on 1/3 of the cookies and you put red sugar on 1/4 of the cookies. How many cookies have both pink frosting and red sugar on them?(a) Is the cookie word problem a problem for 1/3 • 1/4 ? If so, explain briefly whyit is, if not, modify the problem so that it is a problem for 1/3 • 1/4 .(b) Is the cookie word problem a problem for 1/3 + 1/4 ? If so, explain briefly whyit is, if not, modify the problem so that it is a problem for 1/3 + 1/4 .

Answer 1

a) For the cookie to have both pink frosting and red sugar, if we want the probability to be computed using the multiplication law, then the one condition missing in the problem is that the 2 events should be independent events.

Given that the two events are independent, the probability that a cookie has both the things is computed here as: (1/3)*(1/4) = 1/12 is the required probability here.

therefore Revised Problem: How many cookies have both pink frosting and red sugar on them given that both the events are independent of each other.

b) No, the answer is not even 1/3 + 1/4, for this to happen, therefore are 2 conditions required in the question, which are:

• Both the events should be mutually exclusive to each other and
• We would want to know that How many cookies have both pink frosting or red sugar on them. Note that we replaced the AND in original question with OR here.

Therefore revised problem here: How many cookies have both pink frosting or red sugar on them given that both the events are mutually exclusive of each other.