Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be: (i) an even number (ii) a multiple of 3
Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be: (i) an even number (ii) a multiple of 3

Solution:

We know that, there are totally 9 cards from which one card is drawn.

Total number of elementary events = n(S) = 9

(i) From numbers 2 to 10, there are 5 even numbers i.e. 2, 4, 6, 8, 10

So, favorable number of events = n(E) = 5

Hence, probability of selecting a card with an even number = n(E)/ n(S) = 5/9

(ii) From numbers 2 to 10, there are 3 numbers which are multiples of 3 i.e. 3, 6, 9

So, favorable number of events = n(E) = 3

Hence, probability of selecting a card with a multiple of 3= n(E)/ n(S) = 3/9 = 1/3