# A room has three sockets for lamps. From a collection of 10 light bulbs of which 6 are defective, a person selects 3 bulbs at random and puts them in socket. What is the probability that the room - Mathematics and Statistics

Sum

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

#### 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 light bulbs in 10C3 ways.
∴ n(S) = 10C3
∴ Let A be the event that room is lit.
∴ A' is the event that the room is not lit.
For A' 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)
∴ P(Room is lit) = 1 − P(Room is not lit)
∴ P(A) = 1 – P(A')

= 1-(""^6"C"_3)/ (""^10"C"_3)

= 1 - (6xx5xx4)/(10xx9xx8)

= 1-1/6

= 5/6

Concept: Elementary Properties of Probability
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 7 Probability
Miscellaneous Exercise 7 | Q 3 | Page 110