petrifiedbutstanding wrote:
Bunuel wrote:
A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
A. 1/10
B. 3/10
C. 1/2
D. 7/10
E. 9/10
Total = {cake} + {muffin} - {both} + {neither}
100 = 50 + 40 - 20 + {neither} --> {neither} = 30 --> \(\frac{neither}{total}=\frac{30}{100}=\frac{3}{10}\).
Answer: B.
Hope it helps.
Bunuel,
I have a question. I got this right, but I still think I'm missing something. If you considered this in a Venn-diagram format, it would be clear that there can be buyer who purchase cake mix and bread mix or muffin mix and bread mix. This would alter the equation somewhat. And I noticed that you didn't consider this. Can you please explain why?
I'm not sure that I understand what you mean.
We are told that "A certain manufacturer has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix."
So,
Total = {cake} + {muffin} - {both} + {neither} -->
100 = 50 + 40 - 20 + {neither} -->
{neither} = 30.
What should be altered above and why?
You're right actually. I considered buyers of the bread mix as well, which is clearly not necessary in the problem.