Probabilty related question

Question

1. The marriage register data shows that 5 % of male and 0.25 % of female are divorcee. Now let us consider that a divorcee person is chosen at random, what is the probability that the chosen divorcee is a male? (Assume equal male and female are existing in the population.)

Answer 1

Remember, it assumes equal male and female are existing in the population. Therefore:

P(male) = 50%

P(female) = 50%

5% of male are divorcee:

P(male and divorcee) = 5% of 50% =(0.05)(0.5) = 0.025

0.25% of female are divorcee:

P(female and divorcee) = 0.25% of 50% = (0.0025)(0.5) = 0.00125

Those two are mutually exclusive. Therefore the probability of divorcee is:

P(divorcee) = 0.025+0.00125 = 0.02625

This is conditional probability and the formula is:

P(B | A) = P(A and B)/P(B) is read as "The probability of B given A"

The probability of the chosen divorcee is male = The probability of male given he's divorcee.Therefore:

P(male | divorcee) = P(male and divorcee)/P(divorcee)

= 0.025/.02625 = .9524 = 95.24%