The table below contains counts and ratios for a set of data instances to be used for supervised Bayesian learning. The output attribute is sex with possible values male and female. Consider an individual who has said no to the life insurance promotion, yes to the magazine promotion, yes to the watch promotion and has credit card insurance. Use the values in the table together with Bayes classifier to determine which of a,b,c or d represents the probability that this individual is male.

A) 4/6) 2/6) 2/6) 2/6) 6/10) / PE
B) 4/6) 2/6) 3/4) 2/6) 3/4) / PE
C) 4/6) 2/6) 4/6) 2/6) 6/10) / PE
D) 2/6) 4/6) 4/6) 2/6) 4/10) / PE

Question

The table below contains counts and ratios for a set of data instances to be used for supervised Bayesian learning. The output attribute is sex with possible values male and female. Consider an individual who has said no to the life insurance promotion, yes to the magazine promotion, yes to the watch promotion and has credit card insurance. Use the values in the table together with Bayes classifier to determine which of a,b,c or d represents the probability that this individual is male.

A) 4/6) 2/6) 2/6) 2/6) 6/10) / PE 
B) 4/6) 2/6) 3/4) 2/6) 3/4) / PE 
C) 4/6) 2/6) 4/6) 2/6) 6/10) / PE 
D) 2/6) 4/6) 4/6) 2/6) 4/10) / PE

Quizplus · Accepted Answer

We need to calculate P(sex=male | no_life_insurance, magazine=yes, watch=yes, credit_card_insurance=yes) using Bayes classifier. According to Bayes classifier,

P(sex=male | attributes) = P(attributes | sex=male) * P(sex=male) / P(attributes)

We can ignore the denominator as it will be the same for all options. Now, we need to calculate the numerator for each option and choose the one with the highest value.

For option A: 
P(attributes | sex=male) = (4/6) * (2/6) * (2/6) * (2/6) = 16/648
P(sex=male) = 6/10
Numerator = 16/648 * 6/10 = 96/648

For option B:
P(attributes | sex=male) = (4/6) * (2/6) * (3/4) * (2/6) = 24/432
P(sex=male) = 3/4
Numerator = 24/432 * 3/4 = 18/144

For option C:
P(attributes | sex=male) = (4/6) * (2/6) * (4/6) * (2/6) = 64/648
P(sex=male) = 6/10
Numerator = 64/648 * 6/10 = 384/648

For option D:
P(attributes | sex=male) = (2/6) * (4/6) * (4/6) * (2/6) = 64/648
P(sex=male) = 4/10
Numerator = 64/648 * 4/10 = 256/648

Therefore, the option with the highest numerator is C with a value of 384/648. So, the probability that this individual is male is 384/648 or approximately 0.59.

The Table Below Contains Counts and Ratios for a Set