Question

A recent survey was conducted to determine how people consume their news. According to this​ survey, 60​% of men preferred getting their news from television. The survey also indicates that 42​% of the sample consisted of males. ​ Also, 42​% of females prefer getting their news from television. Use this information to answer the following questions.

a. Consider that you have 30000 ​people, given the information​ above, how many of them are​ male?
b. Again considering that you have 30000 ​people, how many of them are​ female?
c. Out of the males in your​ sample, how many of them prefer getting their news on​ television?
d. Out of the males in your​ sample, how many of them prefer getting their news​ on-line?
e. Out of the females in your​ sample, how many of them prefer getting their news on​ television?
f. Out of the females in your​ sample, how many of them prefer getting their news​ on-line?
g. How many people in your sample prefer getting their news from​ television?
h. How many people in your sample prefer getting their news from​ on-line?
nothing
i. Given that a person prefers getting their news on television​, what is the probability that the person is male ​(round to 3 decimal​ places)?

PLEASE SHOW ALL WORK

Answer 1

Assuming that the population prefer getting their news either online or on television

(a)

As 42% of the sample consists of males

Out of 30000 people, the number of male = 0.42*30000 = 12600

(b)

The number of females = (1 - 0.42)*30000 = 17400

(c)

Number of males in the sample who prefer getting their news on television = 0.60*12600 = 7560

(d)

Number of males in sample who prefer getting their news online

= (1 - 0.6)*12600 = 5040

(e)

Number of females who prefer getting their news on television

= 0.42*17400 = 7308

(f)

Number of females who prefer getting their news on line

= (1 - 0.42)*17400 = 10092

(g)

No of people in the sample who prefer getting their news from television = 7560 + 7308 = 14868

(h)

No of people in the sample who prefer getting their news from online

= 5040 + 10092 = 15132

(i)

Let A denote the event that the person is a male

and B denote the event that the person prefer getting news on television

Thus, P(A) = 0.42

P(B|A) = 0.60

P(B|A') = 0.42

Thus, P(B) = P(B|A)*P(A) + P(B|A')*P(A')

= 0.60*0.42 + 0.42*0.58 = 0.4956

The required probability = P(A|B)

= P(B|A)*P(A)/P(B) = 0.508