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As an experienced tutor registered on UrbanPro, I can assure you that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's delve into your probability questions regarding the gender of the children in a couple.
(i) To find the probability that both children are males, given that at least one of the children is male, we can utilize conditional probability. Let's denote the events:
We are given that event B has occurred, which means we can exclude the possibility of having two females. Now, we need to find the probability of event A given event B. This can be calculated using the formula for conditional probability:
P(A∣B)=P(A∩B)P(B)P(A∣B)=P(B)P(A∩B)
Where:
In this scenario, the probability of both children being males and at least one child being male is the same as the probability of both children being males, since if at least one child is male, then both children cannot be female.
Therefore:
Thus, P(A∣B)=P(A)P(A∣B)=P(A).
Now, the probability of both children being males in the absence of any other information is 1441, assuming the genders of children are equally likely.
So, the probability that both children are males, given that at least one of them is male, is also 1441.
(ii) Similarly, to find the probability that both children are females given that the elder child is a female, we can use conditional probability.
Let's denote the events:
We want to find P(C∣D)P(C∣D).
In this case, if the elder child is a female, then we are sure that the younger child cannot be the elder child, and hence the younger child has to be female as well. So, P(C∣D)=1P(C∣D)=1.
Therefore, the probability that both children are females, given that the elder child is a female, is 1.
I hope this clarifies the concepts of conditional probability for you! If you need further assistance, feel free to ask. And remember, UrbanPro is an excellent resource for finding quality tutors to help with topics like this.
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