A binary number is made up of 16 bits. probability of an incorrect bit appearing is p and errors in

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14.Probability

hard

A binary number is made up of $16$ bits. The probability of an incorrect bit appearing is $p$ and the errors in different bits are independent of one another. The probability of forming an incorrect number is

A

$\frac{p}{{16}}$

B

${p^{16}}$

C

${}^{16}{C_1}{p^{16}}$

D

$1 - {(1 - p)^{16}}$

Solution

(d) Probability of correct bit appearing is $(1 -p)$

$\therefore$ Probability of correct number $ = {(1 – p)^{16}}$

and hence probability of incorrect number $ = 1 – {(1 – p)^{16}}$.

Standard 11

Mathematics

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