In a certain city, 55.6% of the residents are male or colorblind. 55.2% of the r
ID: 3275389 • Letter: I
Question
In a certain city, 55.6% of the residents are male or colorblind. 55.2% of the residents are male. 0.1% of the residents are both male and colorblind.
(a) Are the event of being male and the event of being colorblind mutually exclusive? Justify your answer by showing some calculations.
(b) Are the event of being male and the event of being colorblind dependent? Justify your answer by showing some calculations.
(c) What percentage of the residents is colorblind?
(d) What percentage of the residents is female and not colorblind?
Explanation / Answer
a) No, these events aren't mutually exclusive because
P(Male and colorblind) is not equal to 0 so they can occur at the same time.
b) By the formula:
P(Male or colorblind) = P(Male) + P(Colorblind) - P(Male and Colorblind)
So,
P(Colorblind) = 0.556 - 0.552 + 0.001 = 0.005
Now,
P(Colorblind)*P(Male) = 0.005*0.552 = 0.00276 which is not equal to P(Colorblind and male). Hence, these events are not independent.
c) From part b),
P(Colorblind) = 0.005
Hence,
Percentage of colorblind = 0.5%
d) % of residents female and not colorblind
= 100% - % of male or colorblind
= 100% - 55.6%
= 44.4%