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  • The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officiais inspect four of the computers picked at r

The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officiais inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system is deemed functional be denoted by \mathrm{p}. Then \mathrm{100p= }______.

Option: 1

11.9


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{p= } probability of picking ' 3 ' working computers or '4' working computers

Total ways to pick four comp \mathrm{={ }^{10} \mathrm{C}_4 }

Fav. ways for which system to be declared functional = Either all 4 are functional or three of them are functional
\mathrm{={ }^4 C_4+{ }^4 C_3 \times{ }^6 C_1 }

So
\mathrm{p =\frac{\text { fav }}{\text { Total }} }
\mathrm{ =\frac{{ }^4 C_4+{ }^4 C_3 \times{ }^6 C_1}{{ }^{10} C_4}=\frac{25}{210} }

\Rightarrow \mathrm{ 100 p=11.9 }

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