Let the probability p n that a family has exactly n children be α p n , where n ≥ 1 and p 0 = 1 – α p(1 + p + p 2 + .....) (0 < α , p < 1). Giving birth to a boy and girl is equally likely. If k ≥ 1, then find the probability that the family has exactly k boys.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Let E j denote the event that the number of children in the family is j. Let A denote the event that
the family has exactly k boys. We have
P(E j ) = α p j (j = 0, 1, ......) and P(A/E j ) = 
P(A) = 
= 
we know that |x| < 1 and a +ve integer m
(1 – x) –m = 1+ m C 1 x + m + 1 C 2 x 2 + ......
⇒ P(A) = 
= 
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems