In an examination,20 questions of true-false | vedclass

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(A) Let $X$ represent the number of correctly answered questions out of $20$ questions. The repeated tosses of a coin are Bernoulli trials. Since the

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$\frac{1}{2^{20}} \sum_{x=12}^{20} {}^{20}C_{x}$

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(A) Let $X$ represent the number of correctly answered questions out of $20$ questions. The repeated tosses of a coin are Bernoulli trials. Since the student answers randomly based on a coin toss,the probability of answering any question correctly is $p = \frac{1}{2}$.$	herefore q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}$.$X$ follows a binomial distribution with $n = 20$ and $p = \frac{1}{2}$.$	herefore P(X = x) = {}^{20}C_{x} (\frac{1}{2})^{x} (\frac{1}{2})^{20-x} = {}^{20}C_{x} (\frac{1}{2})^{20}$.We need to find the probability that the student answers at least $12$ questions correctly,which is $P(X \geq 12)$.$P(X \geq 12) = P(X = 12) + P(X = 13) + \dots + P(X = 20)$.$P(X \geq 12) = \sum_{x=12}^{20} {}^{20}C_{x} (\frac{1}{2})^{20} = \frac{1}{2^{20}} \sum_{x=12}^{20} {}^{20}C_{x}$.

In an examination,$20$ questions of true-false type 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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