Answer to Question #194945 in Statistics and Probability for Alex

Question

A job interview at a college attracts 100 candidates of which 30% are females and 70% are males. 40% of both female and male candidates have less than 6 months of work experience and the other 60% have at least 6 months of work experience.

If only one of them will be hired, calculate the probability that he/she is a

(i) Male and has less than 6 months of work experience

(ii) Female or has at least 6 months of work experience

Answer 1

Solution :-

Total condidates = 100

which 30% are females and 70% are males

Number of male=70

number of female=30

according to question,40% of both female and male candidates have less than 6 months of work experience.

so

number of male, less than 6 months of work experience=40% of 70= 28

number of female, less than 6 months of work experience=40% of 30= 12

according to question

other 60% have at least 6 months of work experience.

number of male, at least 6 months of work experience=60% of 70= 42

number of female, at least 6 months of work experience=60% of 30= 18

now If only one of them will be hired,

then

(i) probability (Male and has less than 6 months of work experience)=28/100=7/25

(ii) probability (Female or has at least 6 months of work experience)

=(number of female + number of condidate who have atleast 6 month exp. - number of female who have atleast 6 month exp.)/100

=[30+(42+18)-18]/100

=72/100

=18/25