2020_III_12_Probability

2020_III_12_Probability

Could there be a typo in part (i) of this question?
P(T=2)=P(X=2,Y=1)+P(X=1,Y=2)+P(X=2,Y=2)
=qpq+ppq+qppq
=pq(q+p+pq)
=pq(1+(1-q)q)
=pq(1+q-qq)
But the result gives P(T=2)=pq(2-q-qq). Or I’m being an idiot. Either way, put me out of my misery.

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Pinned this to see if anyone else has insight!

I think that P(X=2\cap Y=1)=qp\times p should give you an answer that agrees with their formula.
Hope this helps.

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So I just assumed the question was A wants a head and B wants a tail…oops.

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Here’s my stab at a solution, including the most welcome difference of two squares…

Q12 STEP3 2020.pdf (2.1 MB)

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:clap: Nice!!