From 10 identical cards, numbered 1, 2, 3, ……………, 10, one card is drawn at random. Find the probability that the number on the card drawn is a multiple of :

(i) 2

(ii) 3

(iii) 2 and 3

(iv) 2 or 3

(i) Total number of possible outcomes = 10 (i.e., 1, 2, 3, ……………, 10)

Number of favorable outcomes (Getting a card that is a multiple of 2) = 5 (2, 4, 6, 8, 10)

P(Getting a card that is a multiple of 2) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

= $\dfrac{5}{10}$

= $\dfrac{1}{2}$

Hence, the probability of getting a card that is a multiple of 2 is $\dfrac{1}{2}$.

(ii) Total number of possible outcomes = 10 (i.e., 1, 2, 3, ……………, 10)

Number of favourable outcomes (Getting a card that is a multiple of 3)= 3 (3, 6, 9)

P(Getting a card that is a multiple of 3) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

= $\dfrac{3}{10}$

Hence, the probability of getting a card that is a multiple of 3 is $\dfrac{3}{10}$.

(iii) Total number of possible outcomes = 10 (i.e., 1, 2, 3, ……………, 10)

Number of favourable outcomes (Getting a card that is a multiple of 2 and 3 ) = 1 (6)

P(Getting a card that is a multiple of 2 and 3) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

= $\dfrac{1}{10}$

Hence, the probability of getting a card that is a multiple of 2 and 3 is $\dfrac{1}{10}$.

(iv) Total number of possible outcomes = 10 (i.e., 1, 2, 3, ……………, 10)

Number of favourable outcomes (Getting a card that is a multiple of 2 or 3 ) = 7 (2, 3, 4, 6, 8, 9, 10)

P(Getting a card that is a multiple of 2 or 3 ) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

= $\dfrac{7}{10}$

Hence, the probability of getting a card that is a multiple of 2 or 3 is $\dfrac{7}{10}$.