Question

at seaside farms, there are a number of adult goats and a number of kids (baby goats). some of them are spotted and the rest have solid - colored coats. a goat is chosen at random. let a be the event that the randomly chosen goat is an adult. let b be the event that the randomly chosen goat is spotted. complete the paragraph. the probability of a is 0.625, and the conditional probability of a given b is. so, events a and b must independent.

Explanation:

Step1: Calculate the conditional probability \(P(A|B)\)

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). From the table, \(n(A\cap B) = 60\) (number of adult - spotted goats), and \(n(B)=80\) (total number of spotted goats). So \(P(A|B)=\frac{60}{80}=\frac{3}{4}=0.75\)

Step2: Check for independence

Two events \(A\) and \(B\) are independent if \(P(A|B)=P(A)\). We know \(P(A) = 0.625\) and \(P(A|B)=0.75\). Since \(0.625
eq0.75\)

Answer:

The conditional probability of \(A\) given \(B\) is \(0.75\). So, events \(A\) and \(B\) must not be independent.