Question

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?

Answer 1

The probability that a randomly selected buyer does not purchase either cake mix or muffin mix is 0.30 or 30%.

Step-by-step explanation:

The student's question is about finding the probability that a randomly chosen buyer purchases neither cake mix nor muffin mix. To answer this, we use the principle of inclusion-exclusion in probability.

First, we calculate the total number of buyers purchasing either cake mix or muffin mix, remembering to subtract those who purchase both so as not to count them twice:

• Buyers purchasing cake mix: 50
• Buyers purchasing muffin mix: 40
• Buyers purchasing both: 20

Total buyers purchasing either or both: 50 (cake) + 40 (muffin) - 20 (both) = 70.

Therefore, the number of buyers purchasing neither is the total number of buyers minus those purchasing either or both:

100 (total buyers) - 70 (either or both) = 30 buyers purchase neither.

Finally, we find the probability by dividing the number of buyers who purchase neither by the total number of buyers:

Probability = Number of buyers purchasing neither / Total number of buyers

= 30 / 100

= 0.30 or 30%.