Question

There are 30 scouts and 20 guides in a school. In another school there are 20 scouts and 15 guides. From each school, one student among them is 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

Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

There are 30 scouts and 20 guides in a school. In another school there are 20 scouts and 15 guides.

Solution - (a)

The total number of possible selections are 50×35 = 1750

Solution - (b) What is the probability of both being Scouts?

Number of scouts in first school = 30

Total number of students = 50

So, Probability of selecting a scout = 30/50 = 3/5

Now, Number of scouts in second school = 20

Total number of students = 35

So, Probability of selecting a scout = 20/35 = 4/7

Thus,

Required Probability of both being Scouts is

$\rm \: = \: \dfrac{3}{5} \times \dfrac{4}{7}$

$\rm \: = \: \dfrac{12}{35}$

Solution - (c) What is the probability of both being Guides ?

Number of guides in first school = 20

Total number of students = 50

So, Probability of selecting a scout = 20/50

Now, Number of guides in second school = 15

Total number of students = 35

So, Probability of selecting a guides = 15/35 = 3/7

Thus,

Required Probability of both being guides is

$\rm \: = \: \dfrac{2}{5} \times \dfrac{3}{7}$

$\rm \: = \: \dfrac{6}{35}$

Solution - (d) What is the probability of one scout and one guide ?

Number of scouts in first school = 30

Total number of students = 50

So, Probability of selecting a scout = 30/50 = 3/5

Now, Number of scouts in second school = 20

Total number of students = 35

So, Probability of selecting a scout = 20/35 = 4/7

Number of guides in first school = 20

Total number of students = 50

So, Probability of selecting a scout = 20/50

Now, Number of guides in second school = 15

Total number of students = 35

So, Probability of selecting a guides = 15/35 = 3/7

Thus,

Required Probability is

$\rm \: = \: \dfrac{3}{5} \times \dfrac{3}{7} + \dfrac{2}{5} \times \dfrac{4}{7}$

$\rm \: = \: \dfrac{9}{35} + \dfrac{8}{35}$

$\rm \: = \: \dfrac{17}{35}$