Maharashtra State BoardHSC Science (Electronics) 11th
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A room has three sockets for lamps. From a collection 10 bulbs of which 6 are defective. At night a person selects 3 bulbs, at random and puts them in sockets. What is the probability that roo - Mathematics and Statistics

Sum

A room has three sockets for lamps. From a collection 10 bulbs of which 6 are defective. At night a person selects 3 bulbs, at random and puts them in sockets. What is the probability that room is still dark

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Solution

Total number of bulbs = 10

Number of defective bulbs = 6

∴ Number of non-defective bulbs = 4

3 bulbs can be selected out of 10 bulbs in 10C3 ways.

∴ n(S) = 10C3

Let event A: The room is dark

For event A to happen the bulbs should be selected from the 6 defective bulbs. This can be done in 6C3 ways.

∴ n(A) = 6C3

∴ P(A) = `("n"("A"))/("n"("S"))`

= `(""^6"C"_3)/(""^10"C"_3)`

= `(6 xx 5 xx 4)/(10 xx 9 xx 8)`

= `1/6`.

Concept: Basic Terminologies
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