
Solutions
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problems
 Combined, what was the weight of the
babies at birth?
 Adding the pounds we have 3+2+2+2+3+2+2 =
2(3)+5(2) = 16 lb. Adding the ounces we have
4+11+10+5+3+14+15 = 62. So the answer is 16 lb.,
62 oz. But, 62 oz. = 4 lb., 14 oz., so 20 lb., 14
oz or 20.875 lb. is the total weight. The average
weight is 20.875/7 = 2.98 lb. or 2 lb. 15.7 oz.
or 1.35 kg. The median weight is Nate's, 2 lb.,
14 oz.
 If a woman gives birth to septuplets,
what is the probability that four of them will be
boys and three of them will be girls?
 This is (essentially) the same as asking for the
probability of four heads in seven tosses of a
fair coin. (Girls are slightly more likely to be
born, but the difference between that likelihood
and a 5050 chance are negligible.) There are 128
possible sequences of boys and girls, of which 35
include four boys and 3 girls. So, the correct
answer is = 35/128 = 0.27344. About 3 in 11. Here's a new question:
Is this also the
probability that all seven of them will be boys?
Why (not)?
 What is the probability that the sex
order will be boy  girl  girl  girl  boy 
boy  boy?
 The answer depends on how you interpret the
question. If one assumes that there are four boys
and three girls (and this would have been known
prior to the birth) then proceed as follows.
There are 35 (the same number you see aboveand
for good reason) ways to place the four boys in
four positions in the order. This particular
ordering is exactly one of these 35 ways. So, the
solution is 1 in 35 = 0.02857 or 2.857%.
 Now, if we don't assume there will be four boys
and three girls (that is, we ignore the previous
question), then each child is equally likely to
be either sex. There's only one way for the given
sequence (BGGGBBB) to occur; there are 128
possible sequences (2^{5} = 128). The
probability is then 1/128.
To briefly get technical about it. . .I'm
distinguishing between two probabilities
involving the birth of seven children
> The (unconditional)
probability of the sex order being BGGGBBB (no
information assumed about the prevalence of each
gender)..
> The (conditional)
probability of the sex order being BGGGBBB given
that there are four boys and three girls.
 Here's a new
question: Is the probability that the
order is girl  girl  girl  boy  boy  boy 
boy (that is, "Ladies first!") the
same? Why (not)?
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