First slide

Theorems of probability

Question

Three electric lamps are fitted in a room. 3 bulbs are chosen at random from 10 bulbs having 6 good bulbs. The probability that the room is lighted is

Easy

A

$\frac{29}{30}$
B

$\frac{49}{50}$
C

$\frac{1}{10}$
D

$\frac{43}{66}$

Solution

There are 10 bulbs in which 6 are good, means 4 are not good

$P (R o o m l i g h t e d) = 1 - P (R o o m i s n o t l i g h t e d)$
                                    $= 1 - \frac{4_{C_{3}}}{10_{C_{3}}}$
                                    $= 1 - \frac{1}{30} = \frac{29}{30}$
$∴$ The probability that the room is lighted is   $\frac{29}{30}$

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