cookie question

Question

If I have 2 cookies and I know that 50% of them have raisins and 50% of them have chocolate chips what are the odds for outcome

A) 1 cookie has both chocolate chips and raisins and

B) one cookie has chocolate chips and the other cookie has raisins?

 

what is the math for if we make this question bigger and more complicated, such as we have 100 cookies, 90% have raisins and 50% have chocolate chips? what are the odds of a just raisin, just chocolate chip, a plain cookie and a both topping cookie?

 

Answer 1

The following explanations of parts A) & B) should help with setting up and thinking about the 2nd part of this problem (ask yourself and/or find out from your teacher if a Venn diagram approach is acceptable for the 100 cookie scenario ! ) :

The first of 2 cookies can either be: 

i. Plain 

ii. Only raisins

iii. Only chocolate chips

iv. Both raisins & chocolate chips 

 

Therefore, in order for a 50/50 mix of raisins/chocolate chips to exist for the 2 cookies:

i. 1st plain, 2nd must have both raisins & chocolate chips 

ii. 1st only raisins, 2nd must be only chocolate chips

iii. 1st only chocolate chips, 2nd must have only raisins 

iv. 1st has both raisins/chocolate chips, 2nd must be plain 

This confirms 4 possible combinations exist for the above terms that dictate the cookie scenario:  1. Plain/Both  2. R/CC  3. CC/R  4. Both/Plain 

A) Prob of 1 cookie having Both R & CC (i.e. 1. & 4. of 4 total)  =  2/4  =  1/2  =  50 %

B) Prob of 1 cookie CC, other R (i.e. 2. & 3. of 4 total)  =  2/4  =  1/2  =  50 %

 

* Typically, with a Venn diagram approach to something such as the 2nd part of this cookie problem, you will be provided one of the following 2 sets of additional information in order to make a full determination of the 4 scenarios that are listed: 

a.) amount and/or probability of ONLY raisins 

b.) amount and/or probability of ONLY chocolate chip