A bag contains cards numbered from 1 to 25 . A card is draw at random from the bag . Find the probability that selected card bears number which is multiple of 2 or 3

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Solution

Let E be the event of selecting a card which bears a number which is multiple of 2 or 3.
Favourable outcomes to event E = 2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24
Therefore number of favourable outcomes = 16
And Total number of outcomes = selecting 1 card out of 25 cards = 25
Hence required probability = $\frac{n u m b e r o f f a v o u r a b l e o u t c o m e s}{t o t a l n u m b e r o f o u t c o m e s} = \frac{16}{25}$ (Ans)

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