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explanations and correction to homework 3

# explanations and correction to homework 3 - Explanation to...

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Unformatted text preview: Explanation to 3.17 It seems that there are two diﬀerent understandings on ”eldest daughters”. If ”eldest daughter” include the only daughter in the family, the answer is 0.75. The sample space is {B11 B12, B21, B22, G11, G12, G21, G22}. B or G denote the gender of the selected child. the ﬁrst number after G or B denotes the selected child is the ﬁrst or the second child in their family. The second number denote how many children of the same gender with the selected child are there in their family. For example, B11 denotes the selected child is the only boy in his family. B12 denotes that the selected child is the second child in his family and both children in his family are boys. So the probability of interest is the probability that the selected child is the eldest daughter given that the selected child is a daughter. p=(3/8) / (1/2)=0.75. If ”eldest daughter” means that the child is daughter and is the eldest children. In this case, the probability is 0.5 as in the solutions. Correction to 3.34 I misunderstood ”close”. The correct answer is P (current will ﬂow from s to t) = 1 − P (current wil not ﬂow from s to t) = 1 − P (at least one of 1 and 2 is open)P (relay 3 is open)P (relay 4 is open) = 1 − (1 − 0.4 × 0.6) × (1 − 0.5) × (1 − 0.9) = 0.962 1 ...
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