Q86 / 150 · MHT CET 2016 · Mathematics

Probability of guessing correctly atleast $7$ out of $10$ answers in a "True" or "False" test is = ______

Correct answer
A
$\frac{11}{64}$
B
$\frac{11}{32}$
C
$\frac{11}{16}$
D
$\frac{27}{32}$

Solution

P (x \geq 7) = P (x = 7) + P (x = 8) + P (x = 9) + P (x = 10)

=^{10} C_{7} {(\frac{1}{2})}^{7} {(\frac{1}{2})}^{3} +^{10} C_{8} {(\frac{1}{2})}^{8} {(\frac{1}{2})}^{2} +^{10} C_{9} {(\frac{1}{2})}^{9} {(\frac{1}{2})}^{1} +^{10} C_{10} {(\frac{1}{2})}^{10}

\frac{11}{64}

Hence, the correct answer is option: 'A'.

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