Tom (who is a boy) has two siblings, one older and one younger. We will assume t
ID: 3299995 • Letter: T
Question
Tom (who is a boy) has two siblings, one older and one younger. We will assume that the their genders were determined by the equivalent of a fair coin flip, and that their genders are independent of one another. (a) What is the probability that Tom has two sisters? (b) You are told that Tom comes from a family with at least one girl. What is the probability, conditioned on this information, that Tom has two sisters? (c) You are told that Tom comes from a family where the oldest child is a girl. What is the probability, conditioned on this information, that Tom has two sisters?Explanation / Answer
Question 4:
a) Probability that Tom as 2 sisters
= Probability that older sibling is a female * Probability that the younger sibling is a female
= 0.5*0.5
= 0.25
Therefore 0.25 is the required probability here.
b) Probability that Tom has 2 sisters given that he has at least one sister
= (Probability that he has 2 sisters ) / ( Probability that he has at least one sister )
= (Probability that he has 2 sisters ) / ( 1 - Probability that he has no sister )
= (0.5*0.5)/ (1 - 0.5*0.5)
= 0.25/0.75
= 0.3333
Therefore 0.3333 is the required probability here.
c) Here we are already given that the oldest child is a girl then the younger could be either a girl or a boy with equal probability , therefore the probability that Tom has 2 sisters here is given as: 0.5
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