A die is thrown 7 times. What is the probability that an even number turns up at least 4 times?

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Question: Answered & Verified by Expert

A die is thrown

7

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

4

times?

MathematicsProbabilityBITSATBITSAT 2019

Options:

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

Solution:

2946 Upvotes Verified Answer

The correct answer is:

\frac{1}{2}

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

$= {}^{7}C_{4} {(\frac{1}{2})}^{4} {(\frac{1}{2})}^{3} + {}^{4}C_{5} {(\frac{1}{2})}^{5} {(\frac{1}{2})}^{2} + {}^{7}C_{6} {(\frac{1}{2})}^{6} {(\frac{1}{2})}^{1} + {}^{7}C_{7} {(\frac{1}{2})}^{7}$

$= \frac{1}{2}$

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