Question

If the frequency of having a light colored hair in the human population is 0.4, and that of having dimples is 0.5, then what is the probability that any given individual will have either light colored or dimples or both?

Answer 1

(1) As per the law of addition of Probability:-The Probability of happening either event is the sum of their frequencies. So the probability that any given individual will have either light colored hair or have dimples will be the sum of their respective frequency i.e.0.4 + 0.5 =0.9
(2) As per the Law of multiplication:-
The probability of a given individual having both light colored hair and dimples will be the product of their frequency i.e.=0.4 x 0.5 = 0.2

Answer 2

Explanation:

Firstly all students the correct answer is 0.7 (please do check Answer sheet of TIFR/JGEEBILS-2010)

Solution:

Frequency of having a light colored hair is 0.4

Frequency of having dimples is 0.5.

As the two events are completely independent and both of these represents the recessive conditions of the two trains inherited in the population so Hardy-Weinburg is not applicable.

Thus, According to the  multiplication law the probability of getting either light colored or dimples is: 0.4 + 0.5 = 0.9,

But try to understand that while taking such a case we have also have counted those individuals twice that had both light colored hairs and dimples. So the freq of both must be subtracted.

Thus, Freq. of getting both (light colored and dimples is): 0.4 x 0.5 = 0.2

Thus final freq of getting light colored, dimples or both is: 0.9-0.2 = 0.7

This is the correct solution in case of any query feel free to contact me at 8923944414