Ques : A person has 3 children with atleast one boy . Find the probability of having atleast 2 boys among children (Source : Arun Sharma , Quant Apt for CAT, Problem:14.5)
Solution:
The event is occuring under the following situations :
event 1 :2nd is a boy & 3rd is a girl OR
event 2 : 2nd is a girl and 3rd is a boy OR
event 3 :2nd is a boy & 3rd is a boy
i.e. required prob = 1/2*1/2+1/2*1/2*+1/2*1/2 = 3/4
However,I am unable to understand why we are calculating the prob for event 1 (2nd is a boy & 3rd is a girl ) & event 2 (2nd is a girl and 3rd is a boy) . In my opinion , both represent the same . since the ques is asking about prob of atleast 2 boys , how does the order of girl-boy came in to pic . As per my understanding , prob should be
event 1 :2nd is a boy & 3rd is a girl OR
event 2 : 2nd is a boy & 3rd is a boy
i.e. required prob = 1/2*1/2+1/2*1/2 = 1/2
Please throw some light where i am missing the point .
Any help is appreciated
probability doubt : Need More explanation
This topic has expert replies
I also have doubt on answer.Ques : A person has 3 children with atleast one boy . Find the probability of having atleast 2 boys among children (Source : Arun Sharma , Quant Apt for CAT, Problem:14.5)
According to question
Total number of ways/events: 1B2G, 2B1G, 3B0G ( As it mentioned in question that person has 3 children with atleast 1 B)
Hence No of fav events: 2B1G, 3B0G (atleast 2B among children)
Hence req. prob = 2/3
I do not think order will matter in this case. If it is can anyone tell me why?
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Remember:bitsho wrote:Ques : A person has 3 children with atleast one boy . Find the probability of having atleast 2 boys among children (Source : Arun Sharma , Quant Apt for CAT, Problem:14.5)
Solution:
The event is occuring under the following situations :
event 1 :2nd is a boy & 3rd is a girl OR
event 2 : 2nd is a girl and 3rd is a boy OR
event 3 :2nd is a boy & 3rd is a boy
i.e. required prob = 1/2*1/2+1/2*1/2*+1/2*1/2 = 3/4
However,I am unable to understand why we are calculating the prob for event 1 (2nd is a boy & 3rd is a girl ) & event 2 (2nd is a girl and 3rd is a boy) . In my opinion , both represent the same . since the ques is asking about prob of atleast 2 boys , how does the order of girl-boy came in to pic . As per my understanding , prob should be
event 1 :2nd is a boy & 3rd is a girl OR
event 2 : 2nd is a boy & 3rd is a boy
i.e. required prob = 1/2*1/2+1/2*1/2 = 1/2
Please throw some light where i am missing the point .
Any help is appreciated
P(good outcome) = 1 - P(bad outcome)
It's given that we have at least one boy. The question is really asking:
What is the probability that at least 1 of the other 2 children is a boy?
The only bad outcome is if the two other children are girls: 1/2 * 1/2 = 1/4.
So P(at least one additional boy) = 1 - 1/4 = 3/4.
Also, remember that:
P(A and B) = P(A) * P(B)
To determine the probability of events happening together, we have to determine the probability of each separate event and multiply -- and we have to account for all the different ways those separate events could occur.
So P(at least 1B) = P(B) * P(G) + P(G) * P(B) + P(B) * P(B)
Of course, it's much simpler to use the method I described above.
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Hi,bitsho wrote:Ques : A person has 3 children with atleast one boy . Find the probability of having atleast 2 boys among children (Source : Arun Sharma , Quant Apt for CAT, Problem:14.5)
where does it say that there's an equal chance that any child is a boy or girl? All the solutions assume that there's a 50/50 chance, but it doesn't say so explicitly.
Without that information, the question is unanswerable.
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