NIMCET 2012 Question Paper with solutions

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Question : 37 of 120

Marks: +1, -0

If a fair coin is tossed n times, then the probability that the head comes odd number of times is

$1/2$
$1/2^n$
$1/2^{n-1}$
None of these

Solution:

Here, p =

1/2

and q =

1/2

Now, by binomial distribution
=

↖{n}C_1(p)^1 (q)^{n-1}

+

↖{n}C_3(p)^3(q)^{n-3}

+

↖{n}C_5(p)^5(q)^{n-1}

+ ...
=

↖{n}C_1 (1/2)^1 (1/2)^{n-1}

+

↖{n}C_3 (1/2)^3 (1/2)^{n-3}

+

↖{n}C_5 (1/2)^5 (1/2)^{n-5}

+ ...
=

↖{n}C_1 (1/2)^n

+

↖{n}C_3(1/2)^n

+

↖{n}C_5 (1/2)^n

+ ...
=

(1/2)^n

{

↖{n}C_1+\,↖{n}C_3+\,↖{n}C_5+...

}
=

2/2^n . (2^{n-1})

=

1/2

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