Probability
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Q.

In a game there are 70 people in which 40 are boys and 30 are girls, out of which 10 people are selected at random. One from the total group, thus selected is selected as a leader at random. What is the probability that the person, chosen as the leader is a boy?

 A.

4/7

 B.

4/9

 C.

5/7

 D.

2/7

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Solution:
Option(A) is correct

The total groups contains boys and girls in the ratio $4:3$

If some person are selected at random from the group, the expected value of the ratio of boys and girls will be $4:3$

If the leader is chosen at random from the selection, the probability of him being a boy = 4/7


(5) Comment(s)


Prob
 ()

Sorry, option B) 4/9 can be ruled out as it is



Mayukh Mitra
 ()

if 4:3 is taken as the same ratio in a group of 10 people then it would give sum of 7 people which is less than 10. also if you assume x as no.of boys and x-10 as no.of girls then that would result in total of 35 people since x would be equal to 5. so if we walk with 4:3 then total gives 7. therefore 3 people must either boys or girls. so the ratio would become 4:6 or 7:3 so that equation satisfies.


Rio
 ()

I believe you have a messed up notion about the 'ratio'. It is like percentage. You do not necessarily deal with the actual numbers, you try to analyse the scenario.


Giree
 ()

Could not accept that presumed 4:3 for 10 persons selected


Prob
 ()

We expect the probability to be more than 50% as there are more number of boys than girls.

D) 2/7- too low, ruled out

B)5/9- We will have 7 in the denominator (from 70C10) as it can't cancel out, so ruled out.

After this 5/7 seems too high so went with 4/7.

I know it isn't a great approach but can come handy when the time is limited.