Question

a - likes asparagus
b - likes broccoli
c - likes carrots
there are 28 students
in the class.
what is p(not b | not a)?

Explanation:

Step1: Calculate \(n(\text{not }A)\)

The total number of students is \(28\). The number of students who like asparagus (\(A\)) is \(3 + 1+2 + 4=10\). So, \(n(\text{not }A)=28 - 10=18\).

Step2: Calculate \(n(\text{not }A\text{ and not }B)\)

The number of students who like broccoli (\(B\)): \(2 + 1+4+3 = 10\). The number of students who like neither \(A\) nor \(B\) is \(4 + 6+5=15\) (the regions outside \(A\) and \(B\)).

Step3: Use the conditional - probability formula

The formula for conditional probability is \(P(\text{not }B|\text{not }A)=\frac{n(\text{not }A\text{ and not }B)}{n(\text{not }A)}\). Substitute \(n(\text{not }A\text{ and not }B) = 13\) (from the Venn - diagram regions outside \(A\) and \(B\): \(4 + 5+4\)) and \(n(\text{not }A)=18\) into the formula.

Answer:

\(\frac{13}{18}\)