Question

A frozen yogurt shop sells only chocolate and vanilla frozen yogurt. On average, 60% of customers order chocolate yogurt, and 40% of customers order vanilla yogurt. In the following random number table, any number contains:

A. Chocolate yogurt
B. Vanilla yogurt
C. Both chocolate and vanilla yogurt
D. Neither chocolate nor vanilla yogurt

Answer 1

To determine the probability of a cookie containing chocolate or nuts, or neither, one applies the addition rule for probabilities. For chocolate or nuts, it's 40%, and for neither, it's 60%.

Step-by-step explanation:

The question from the student asks to find the probability that a cookie contains either chocolate or nuts, and the probability that a cookie contains neither. This is a classic example of problems dealing with probability in mathematics, specifically about the addition rule for probabilities.

To solve part a, we can use the formula P(A or B) = P(A) + P(B) - P(A and B). Here, P(chocolate or nuts) = P(chocolate) + P(nuts) - P(both chocolate and nuts).

To answer part a: P(chocolate or nuts) = 0.36 + 0.12 - 0.08 = 0.40 or 40%.

For part b, the probability that a cookie does not contain chocolate or nuts can be found by subtracting the probability of part a from 1, as these are complementary events.

To answer part b: P(neither chocolate nor nuts) = 1 - P(chocolate or nuts) = 1 - 0.40 = 0.60 or 60%.