If getting a head on a fair coin when it is tossed is considered as success, then the probability of having more number

Question

If getting a head on a fair coin when it is tossed is considered as success, then the probability of having more number of failures when ten fair coins are tossed simultaneously is k , then $512 k$ is ________

Smart Achievers · Accepted Answer

(193)

$P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)$

$= {(\frac{1}{2})}^{10} + {}^{10}C_{1} {(\frac{1}{2})}^{9} (\frac{1}{2}) + {}^{10}C_{2} {(\frac{1}{2})}^{8} {(\frac{1}{2})}^{2} + {}^{10}C_{3} {(\frac{1}{2})}^{7} {(\frac{1}{2})}^{3} + {}^{10}C_{4} {(\frac{1}{2})}^{6} {(\frac{1}{2})}^{4} = \frac{193}{2^{9}}$

Solution

Q.
If getting a head on a fair coin when it is tossed is considered as success, then the probability of having more number of failures when ten fair coins are tossed simultaneously is k , then $512 k$ is ________

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Solution

Q. If getting a head on a fair coin when it is tossed is considered as success, then the probability of having more number of failures when ten fair coins are tossed simultaneously is k , then 512k is ________

Ans. (193) P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4) =(12)10+C110(12)9(12)+C210(12)8(12)2+C310(12)7(12)3+C410(12)6(12)4=19329

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Q.
If getting a head on a fair coin when it is tossed is considered as success, then the probability of having more number of failures when ten fair coins are tossed simultaneously is k , then $512 k$ is ________