Question

There is a working women's hostel in a
town, where 75% are from neighbouring
town. The rest all are from the same town.
48% of women who hail from the same
town are graduates and 83% of the women
who have come from the neighboring town
are also graduates. Find the probability that
a woman selected at random is a graduate
from the same town.​

Answer 1

Let the total number of women be equal to x .

No. of women the same town = 25x/100 =0.25x

No. Of women from the neighbouring town = 75x/100

= 0.75x

No. of women the same town who are graduate = 0.25x × 48/100

= 0.12 x

No. Of women from the neighbouring town who are graduates = 0.75x × 83/100

= 0.6225x

probability that a woman selected at random is a graduate from the same town -

=> (0.25x × 0.12x)/(0.25x × 0.12x)(0.75x × 0.6225x)

=> 0.0603