Question

given the following venn diagram

answer the following questions by filling in each box with the appropriate value.

a) ( p(a cup b)=)

b) ( p(a ) but not ( b)=)

c) ( p(b ) but not ( a)=)

d) ( p ) (neither ( a ) nor ( b)=)

Explanation:

Step1: Calculate \(P(A\cup B)\)

The formula for \(P(A\cup B)\) using Venn - diagram values is \(P(A\cup B)=P(A - B)+P(A\cap B)+P(B - A)\).
Substitute the values: \(P(A - B) = 0.39\), \(P(A\cap B)=0.27\), \(P(B - A)=0.18\).
\(P(A\cup B)=0.39 + 0.27+0.18\)

$$P(A\cup B)=0.84$$

Step2: Calculate \(P(A\text{ but not }B)\)

\(P(A\text{ but not }B)\) is the part of \(A\) that does not overlap with \(B\). From the Venn - diagram, it is directly given as \(0.39\).

Step3: Calculate \(P(B\text{ but not }A)\)

\(P(B\text{ but not }A)\) is the part of \(B\) that does not overlap with \(A\). From the Venn - diagram, it is directly given as \(0.18\).

Step4: Calculate \(P(\text{neither }A\text{ nor }B)\)

It is given as \(0.16\) in the Venn - diagram (the value outside both \(A\) and \(B\)).

Answer:

a) \(0.84\)
b) \(0.39\)
c) \(0.18\)
d) \(0.16\)