Question

given the following venn diagram: data answer the following questions by filling in each box with the appropriate value. a) ( p(acup bcup c)=) b) ( p(b) but not ( c)=) c) ( p(c) but not ( a)=) d ( p(acap bcap c)=)

Explanation:

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

Sum all the probabilities in the Venn - diagram regions: \(0.46 + 0.09+0.07 + 0.11+0.06+0.05 + 0.14+0.02\)

$$
LATEXBLOCK0
$$

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

Sum the regions that are in \( B \) but not in \( C \). That is \(0.09 + 0.07\)

$$0.09+0.07 = 0.16$$

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

Sum the regions that are in \( C \) but not in \( A \). That is \(0.14+0.02 + 0.05\)

$$0.14+0.02+0.05=0.21$$

Step4: Calculate \( P(A\cap B\cap C) \)

The region that is common to \( A\), \( B\) and \( C\) is \(0.06\)

Answer:

a) \(1\)
b) \(0.16\)
c) \(0.21\)
d) \(0.06\)