Question

There are 30 scouts and 20 guides in school. In another there are 20 scouts and 15 guides. From each school, students among them are to be selected for participation in a seminar.
a.What is the total number of possible selections?
b.What is the probability of both being scouts?
c.What is the probability of both being guides?
d.What is the probability of one scout and one guide?

Answer 1

Hint: In order to solve this problem, the total number of possible selections can be calculated as the product of the total number of scouts and guides from both the schools.
Probability can be calculated by the formula given below:-
 $Probability = \dfrac{{no.of.Possible Outcome}}{{Totalno.ofoutcome}}$
Participation because of one scout and one guide = (scout from School A) × (guide from School B) × (scout from School B) × (guide from School A).

Complete step-by-step answer:
In course of solving this problem related to probability, we are asked several questions which are answered as follows:-

	School A	School B	Total
Number of Scouts	30	20	50
Number of Guides	20	15	35
Total	50	35	85

Given: -
a.) Total no. of possible selection = 50 $ \times $ 35 = 1750

b.) Both of them being scout is 30 $ \times $ 20 = 600
      ∴ Probability of both being scout$ = \dfrac{{600}}{{1750}} = \dfrac{{12}}{{35}}$

c.) Both of them being guides is 20 × 15 = 300

      ∴ Probability of both being guides= (300/1750) = (6/35)

d.) participation when one being scout and one being guide = (scout from School A) × (guide from School B) × (scout from School B) × (guide from School A)
=(30 × 15) +(20 × 20)
=450 + 400
=850.
∴Probability of one being scout and one being guide is given by:-
$ = \dfrac{{850}}{{1750}}$
$ = \dfrac{{17}}{{35}}$

Note: The probability of an event is defined to be the ratio of the number of cases favourable to the event—i.e., the number of outcomes in the subset of the sample space defining the event—to the total number of cases. The formula for probability is given by:-
$Probability = \dfrac{{no.of.Possible Outcome}}{{Totalno.ofoutcome}}$