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# S1 Probability Question Watch

1. Here is the question and solutions.
Can anyone explain the reasoning behind the answer to part d)
I don't get it
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2. I actually used a tree diagram as I found it helped better with part d.
Thinks of it this way:
I'll use ¬ to represent NOT
there are 4 ways of getting only 1 wife and 1 husband retired when you pick 2 couples, they are WH and ¬W¬H, or ¬W¬H and WH (the reverse order to the first pick)
or ¬WH and W¬H or W¬H and ¬WH (again the reverse)
the first duplicated pair require a non-retired couple AND a fully retired couple 0.32 x 0.22
the 2nd duplicated pair require one retired but not the other (both ways round) 0.08 x 0.38
So overall we need double these 2 pairs (i.e. to take account of the order selected), so 2 x ((0.32 x 0.22) + (0.08 x 0.38))
If this doesn't sound too clear, draw a tree.
Bric

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Updated: April 12, 2013
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