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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Probability
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Q)

A fair coin is tossed 10 times. The probability that the coin shows head exactly 4 times is

$\begin {array} {1 1} (A)\;\large\frac{105}{512} & \quad (B)\;\large\frac{103}{512} \\ (C)\;\large\frac{101}{512} & \quad (D)\;None\: of \: these \end {array}$

 

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A)
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Here $ n = 10$
P = P( getting a head in a single trial )
$ \Rightarrow P = \large\frac{1}{2}$
$ Q = \large\frac{1}{2}$
Hence $ P(4)=10C_4 \bigg( \large\frac{1}{2} \bigg)^4 \bigg( \large\frac{1}{2} \bigg)^6$
$ = \large\frac{210}{1024}$
$ = \large\frac{105}{512}$
Ans : (A)
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