Question

In a certain office, we have 30 female workers and 70 male workers. The probability

of having a smoker worker given that he is a male is 0.6 and the probability of having a
smoker worker given that she is a female is 0.4. Select a person at random from this office.
Find
a.The probability that this person will be a smoker.
b.Given that this person is a smoker, what is the probability that this person will be a male.
c. The probability that this person will be a smoker or a male

Answer 1

Explanation:

a)

P(f ) = probability of being female = .3

P(m ) Probability of being male = .7

P(s/m) = probability of having a smoker worker given that he is a male = .6

P(s/f) = probability of having a smoker worker given that he is a male = .4

p(s) = p(m) x p(s/m) + p(f) x P(s/f)

= .7 x .6 + .4 x .3

= .42 + .12

= .54

b )

p (m/s) = probability that this person will be a male,Given that this person is a smoker

p(m) x p(s/m) / [ p(m) x p(s/m) + p(f) x P(s/f) ]

= .7 x .6 / .7 x .6 + .4 x .3

= .42 / .54

= .78

c )

Probability of the person being a smoker and male

= .54 x .78 = .42

probability of a person being a male and non smoker = .7 - .42 = .28

probability of a person being a non smoker and female = .46 -.28 =.18

probability that person will be a smoker or a male

= 1 - (a person being a non smoker and female).

= 1 - .18

= .82 .