NIMCET 2009 Question Paper with solutions

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Question : 29 of 120

Marks: +1, -0

A

and

B

throw a die in succession to win a bet with

A

starting first. Whoever throws '1' first wins an amount of

₹ 110 .

What are the respective expectations of

A

and

B

?

$₹ 70$ and $₹ 40$
$₹ 60$ and $₹ 50$
$₹ 75$ and $₹ 35$
None of these

Solution:

P(1)=\;{1}/{6} ; P(\ov{1})=\;{5}/{6}

P(A

wins

)=\;{1}/{6}+\;{5}/{6} × \;{5}/{6} × \;{1}/{6}+. . .

=\;{1}/{6}[1+\;{25}/{36}+(\;{25}/{36})^{2}+. . .]

=\;{\;{1}/{6}}/{1-\;{25}/{36}}=\;{1 \/ 6}/{11 \/ 36}=\;{6}/{11}

P(B

wins

)=1-P(A

wins

)

=1-\;{6}/{11}=\;{5}/{11}

E(

amount of

A)=110 × \;{6}/{11}=60

E(

amount of

B)=110 × \;{5}/{11}=50

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