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Probability Ncert Solutions Maths class 12th Maths Class 12th Probability

72. In an examination, 20 questions of true-false are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’, if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.

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alok kumar singh | Contributor-Level 10

4 months ago

72. Let X represent the number of correctly answered questions out of 20 questions.

The repeated tosses of a coin are Bernoulli trails. Since “head” on a coin represents the true answer and “tail” represents the false answer, the correctly answered questions are Bernoulli trials.

$\begin{array}{l} ∴ P = \frac{1}{2} \\ ∴ q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2} \end{array}$

X has a binomial distribution with n=20 and $P = \frac{1}{2}$

$∴ P = (X = x) = {nC}_{x}$
$q^{n - x} . p^{x},$ where $x = 0, 1, 2, . . . n$

$= {20C}_{x}$

${(\frac{1}{2})}^{20 - x} . {(\frac{1}{2})}^{x} = {20C}_{x}$
$\begin{array}{l} {(\frac{1}{2})}^{20} \end{array}$

P (at least 12 questions answered correctly) $= P (X \geq 12)$

$= P (X = 12) + P (X = 13) + . . . + P (X = 20) = {20C}_{12}$

${(\frac{1}{2})}^{20} + {20C}_{13}$
${(\frac{1}{2})}^{20} + . . . + {20C}_{20}$
${(\frac{1}{2})}^{20} = {(\frac{1}{2})}^{20} . [20 C_{12}$
$+ {20C}_{13}$
$+ . . . + {20C}_{20}$
$\begin{array}{l} ] \end{array}$

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72. In an examination, 20 questions of true-false are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’, if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.

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