Problem Solving

Hi,

My answer was B) by... 0.5*0.9=0.54+0.05=0.59 but the corect answer was A) - can anyone help please?


Of a group of people surveyed in a political poll, 60 percent said that they would vote for candidate R. Of those who said they would vote for R. 90 percent actually voted for R. and of those who did not say that they would vote for R. 5 percent actually voted for R. What percent of the group voted for R?
(A) 56% (B) 59% (C) 62%
(D) 65% (E) 74%

dunkin77 wrote:Hi,

My answer was B) by... 0.5*0.9=0.54+0.05=0.59 but the corect answer was A) - can anyone help please?


Of a group of people surveyed in a political poll, 60 percent said that they would vote for candidate R. Of those who said they would vote for R. 90 percent actually voted for R. and of those who did not say that they would vote for R. 5 percent actually voted for R. What percent of the group voted for R?
(A) 56% (B) 59% (C) 62%
(D) 65% (E) 74%

5 % of people who did vote for R inspite of saying no wuld equal to =0.4*0.05 = 0.02

so ur answer is 0.6*0.9+0.02=0.56 ...A

ohh - I see - thank yoU!

Let the total number of people that took the survey be n. Also let x and y represent the total number of people who said they would vote for candidate R and those who didn't say they will vote for R respectively.
from the question,
x=60% of n
i.e x=0.6n and
y=(100-60)% of n = 40% of n
i.e y=0.4n
Now, the number of people who actually voted for R is = 90% of x + 5% of y
=0.9x + 0.05y
=0.9(0.6n) + 0.05(0.4n)
=0.54n + 0.02n
=0.56n
= $$\frac{56}{100}n$$
$$i.e\ 56\%\ of\ n$$
the correct answer is A

(90% of 60) + (5% of 40) =>

.9 * 60 + .05 * 40 =>

54 + 2 =>

56