The probability of guessing correctly at leas | vedclass

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(A) This is a binomial distribution problem where $n = 10$ and the probability of success $p = \frac{1}{2}$ (since it is a True/False test). The proba

Vedclass · Accepted Answer

$\frac{11}{64}$

Vedclass · Answer

(A) This is a binomial distribution problem where $n = 10$ and the probability of success $p = \frac{1}{2}$ (since it is a True/False test). The probability of failure is $q = 1 - p = \frac{1}{2}$.We need to find $P(X \geq 7) = P(X=7) + P(X=8) + P(X=9) + P(X=10)$.The formula for binomial probability is $P(X=k) = {}^{n}C_{k} p^{k} q^{n-k}$.$P(X=7) = {}^{10}C_{7} (\frac{1}{2})^{7} (\frac{1}{2})^{3} = \frac{120}{1024}$.$P(X=8) = {}^{10}C_{8} (\frac{1}{2})^{8} (\frac{1}{2})^{2} = \frac{45}{1024}$.$P(X=9) = {}^{10}C_{9} (\frac{1}{2})^{9} (\frac{1}{2})^{1} = \frac{10}{1024}$.$P(X=10) = {}^{10}C_{10} (\frac{1}{2})^{10} (\frac{1}{2})^{0} = \frac{1}{1024}$.Summing these probabilities: $P(X \geq 7) = \frac{120 + 45 + 10 + 1}{1024} = \frac{176}{1024} = \frac{11}{64}$.

The probability of guessing correctly at least $7$ out of $10$ answers in a "True" or "False" test is = $ . . . . . . $

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