A die is thrown 7 times. What is the probability that an even...

A die is thrown

7

times. What is the probability that an even number turns up at least

4

times?

Options

A $\dfrac{1}{2}$
B $\dfrac{31}{64}$
C $\dfrac{51}{128}$
D $\dfrac{35}{128}$

Correct answer

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

Step-by-step solution

For atleast $4$ times an even number, probability is

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

$= \dfrac{1}{2}$

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