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

Step-by-step 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.