A coin is tossed 7 times. Each time a man calls head. The...

A coin is tossed

7

times. Each time a man calls head. The probability that he wins the toss at least four times is

Options

A $\dfrac{1}{4}$
B $\dfrac{5}{8}$
C $\dfrac{1}{2}$
D $\dfrac{1}{6}$

Correct answer

C. $\dfrac{1}{2}$

Step-by-step solution

The man has to win atleast $4$ times.

$∴$ Required probability

$= C4 7 \left(\dfrac{1}{2}\right)^{4}\left(\dfrac{1}{2}\right)^{3} + C5 7 \left(\dfrac{1}{2}\right)^{5}\left(\dfrac{1}{2}\right)^{2} + C6 7 \left(\dfrac{1}{2}\right)^{6}\left(\dfrac{1}{2}\right) + C7 7 \left(\dfrac{1}{2}\right)^{7}$

$= \left(C4 7 + C5 7 + C6 7 + C7 7\right) \times \dfrac{1}{27} = \dfrac{64}{27} = \dfrac{1}{2}$

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