Kushchokhani wrote:
A box contains n shirts, of which 60% are white in color. Three out of every four non-white shirts have a tailoring defect. What percentage of white shirts do not have a tailoring defect?
(1) If one shirt is selected at random from the box, the probability that it will have a tailoring defect is 0.5
(2) The probability that a shirt with tailoring defect will be white in color is 2/5
Good question! IMO D as well.
We know that 60% of n shirts are white in colour. So 3n/5 shirts are white. And 2n/5 shirts are non-white.
p(non white shirt with tailoring defect) = 3/4
So total non white shirts with tailoring defects are 3/4*2n/5 = 3n/10.
Statement 1: If one shirt is selected at random from the box, the probability that it will have a tailoring defect is 0.5
So total defect shirts(white+non white) = n/2. Out of these n/2 shirts defect shirts, 3n/10 shirts are non white defects. So shirts with white defects = \(\frac{n}{2}-\frac{3n}{10} = 0.2n\) shirts.
% of white defect shirts: \((\frac{0.2n}{n})*100=20\)%
Statement 2: The probability that a shirt with tailoring defect will be white in color is 2/5
White shirts=3n/5, Non white shirts=2n/5
Non white shirts with defects= \(\frac{3}{4}*\frac{2n}{5}=\frac{3n}{10}\)
Given: p(white shirt with tailoring defect)=2/5
# white shirts with tailoring defect/All shirts with tailoring defect = 2/5
Let # white shirts with tailoring defect=a
\(\frac{a}{(3n/10+a)}=\frac{2}{5}\).....(Non white shirts with defects=3n/10)
\(5a=\frac{6n}{10}+2a\)
\(a=\frac{2n}{10}\)
% of white defect shirts: (0.2n/n)*100=20%
Thus, option D.