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

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Probability of guessing correctly atleast

7

out of

10

answers in a "True" or "False" test is = ______

MathematicsProbabilityMHT CETMHT CET 2016

Options:

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

Solution:

2654 Upvotes Verified Answer

The correct answer is:

\frac{11}{64}

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}

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