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  • The probability that a man can hit a target is . He tries 5 times. The probability that he will hit the target atm

The probability that a man can hit a target is 3 / 4. He tries 5 times. The probability that he will hit the target atmost one time, is
 

Option: 1

\left(\frac{3}{4}\right)^5
 


Option: 2

\left(\frac{1}{4}\right)^3
 


Option: 3

\left(\frac{1}{4}\right)^2\left(\frac{3}{4}\right)^3
 


Option: 4

None of these


Answers (1)

best_answer

Given, probability that a man can hit a target,

\mathrm{ P(A)=\frac{3}{4} }

\mathrm{\therefore \quad P(\bar{A})=1-P(A)=1-\frac{3}{4}=\frac{1}{4}}

\because He tries 5 times.

\mathrm{ \therefore \quad n=5 }

Let X represent the number of times he hits the targets.

\mathrm{\therefore \quad P(X =r)={ }^5 C_{r}\left(\frac{3}{4}\right)^r\left(\frac{1}{4}\right)^{5-r} }

\mathrm{\therefore \quad P(X =r \leq 1)=P(0)+P(1) }

\mathrm{ =\left(\frac{1}{4}\right)^5+5\left(\frac{3}{4}\right)^1\left(\frac{1}{4}\right)^4 }

\mathrm{ =\left(\frac{1}{4}\right)^4\left(\frac{1}{4}+\frac{15}{4}\right)=\left(\frac{1}{4}\right)^4 \times 4 }

\mathrm{ =\left(\frac{1}{4}\right)^3}

Hence option 2 is correct.






 

Posted by

shivangi.bhatnagar

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