Question

the central board of secondary education has a waiting list of exam of 150 persons. Out of these, 60 are women and 90 are men. One examiner is selected to replace an examiner who has not reported at the centre, find the probability that the examiner selected is a :
(i)woman (ii)man.

Answer 1

the central board of secondary education has a waiting list of exam of 150 persons. Out of these, 60 are women and 90 are men. One examiner is selected to replace an examiner who has not reported at the centre, find the probability that the examiner selected is a :
(i)woman (ii)man. answers is man

Answer 2

Given,

The central board of secondary education has a waiting list of examiners of 150 persons. Out of these, 60 are women and 90 are men.

To Find,

The probability that the examiner selected is a :

(i)woman (ii)man

Solution,

We can solve the question as follows:
It is given that the total number of examiners is 150. Out of these, 60 are women and 90 are men. We have to find the probability that the examiner selected is an (i) woman, (ii) man.

Now,

We know that the probability of an event occurring is given as the number of favorable outcomes divided by the total number of outcomes.

$Probability, P = \frac{Number\: of\: favourable \: outcomes}{Total \: number \: of \: outcomes}$

Now, using the above formula

(i) The probability that the examiner selected a woman is:

The total number of women = 60

The total number of persons on the waiting list = 150

Probability that the examiner selected a woman = Number of women/Total        

                                                                                    number of persons

                                                                                 $= \frac{60}{150}$

                                                                                 $= \frac{2}{5}$

(ii) The probability that the examiner selected a man is:

The total number of women = 90

The total number of persons on the waiting list = 150

Probability that the examiner selected a woman = Number of man/Total        

                                                                                    number of persons

                                                                                 

                                                                                 $= \frac{90}{150}$

                                                                                 $= \frac{3}{5}$

Hence, the probability that the examiner selected is an (i)woman is 2/5  (ii)man is 3/5.