Question

Use the following information to solve the next five exercises. Forty-eight percent of all Californians registered voters prefer Proposition A. Among Latino California registered voters, 55% prefer Proposition A. Thirty-nine percent of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring Proposition A. L = Latino Californians. Suppose that one Californian is randomly selected.

a. Find P(C).

b. Find P(C|L).

c. Find P (L AND C).

d. Are L and C independent events? Show why or why not. e. Are L and C mutually exclusive events? Show why or why not.

Answer 1

48% of Californians registered voters prefer Proposition A

55% of Latino california registered voters prfer Proposition A

39% of Californians are Latino

Given

C = Californians (registered voters) preferring Proposition A.

L = Latino Californians

(i) P(C) = P (Californians (registered voters) preferring Proposition A) = 48/100 = 0.48

(ii)

  

But,

=P(getting a Latino) P(Selected Latino is a californian prefering Proposition A)

= 0.39 x 0.55

P(L) = 0.39

Hence,

  

(iii)

P(L and C) = = 0.39 x 0.55 = 0.2145

(iv)

If L and C are indepedent, P(C/L)=P(C)

Here, P(C/L) = 0.55 is not equal to P(C) = 0,48. Hence L and C are NOT independent.

(v)

If L and C are mutually exclusive,

,

But here . Hence L and C are NOT mutually exclusive.