A room has three electric lamps. From a collection of $10$ electric bulbs of which $6$ are good. $3$ are selected at random & put in the lamps. Find the probability that the room is lighted.

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Solution

Solution -
If one of the three lamps will be lighted, then the
room will be lighted
Probability of picking a good lamp $= \frac{6}{10}$
Probability room will be lighted $= 1 - P (N o l i g h t e d)$
$= 1 - \frac{^{4} C_{3}}{^{10} C_{3}}$
$= 1 - \frac{4}{120}$
$= \frac{29}{30}$

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A room has three electric lamps. From a collection of 10 electric bulbs of which 6 are good. 3 are selected at random & put in the lamps. Find the probability that the room is lighted.

Solution -If one of the three lamps will be lighted, then the room will be lightedProbability of picking a good lamp =610Probability room will be lighted =1−P(Nolighted)=1−4C310C3=1−4120=2930

A room has three electric lamps. From a collection of $10$ electric bulbs of which $6$ are good. $3$ are selected at random & put in the lamps. Find the probability that the room is lighted.

Solution -
If one of the three lamps will be lighted, then the
room will be lighted
Probability of picking a good lamp $= \frac{6}{10}$
Probability room will be lighted $= 1 - P (N o l i g h t e d)$
$= 1 - \frac{^{4} C_{3}}{^{10} C_{3}}$
$= 1 - \frac{4}{120}$
$= \frac{29}{30}$