using venn diagrams

A U B = A+ B - (A and B) = 50+40-20 = 70

Not A and Not B = 100-70 = 30

Probability of Not A and Not B = 30/100 = 3/10

I have attached the Venn diag.

Important point to observe in the question.
1. The question says 50 purchase cake mix and 40 purchase muffin mix.
Whenever u see a sentence like above, where the key word "only" is missing, assume that the number is a combo of "only" + "both" (or all 3)

So in this case, 50 includes ppl who bought ONLY cake mix + those who bought cake mix and muffin mix.

With this u can easily plug in the venn diagram.

a) first plugin in the value of 20 in the intersection of cake and muffin,
b) Now subtract 20 from 50 and 40 respectively and plugin to the respective circles.
c). Subtract the total of 3 values from 100. This is the "None" value, which is outside of all circles.

So we can easily find the probability:
30/100 = 3/10

HT Helps

Good luck

vittalgmat has given a good explanation on solving the problem using Venn Diagram. The other way to solve this question is by using the following equation

Total = A+B+Neither-Both

Total = customer purchasing cake mix + customers purchasing muffin mix + customers purchasing neither cake or muffin mix - customers purchasing both cake and muffin mix

100 = 50 + 40 + N - 20

N = 30

Probability of neither = 30/100 or 3/10

Thank you sooooooo much everyone

except vital gmat who went to the extent of makin a diagram

THANK OU

Is easy

C ake 50
M uffin 40
B oth 20
Total 100
No cake and muffin ?

Remember the formula

C-B + B + M-B + ? = TOTAL

50 – 20 +20 + 40-20 + ? = 100

RESULT:
?= 30

SO THE PROBABILITY IS

PART/ WHOLE ….. 30/100

3/10
THE ANSWER IS C