Thirty identical cards are marked with numbers 1 to 30. If one card is

1.	Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is:(i) a multiple of 4 or 6 (ii) a multiple of 3 and 5 (iii) a multiple of 3 or 5
Answer» There are 30 cards from which one card is drawn . Total number of elementary events = n(S) = 30 (i) From numbers 1 to 30, there are 10 numbers which are multiple of 4 or 6 i.e. {4, 6, 8, 12, 16, 18, 20, 24, 28, 30} Favorable number of events = n(E) = 10 Probability of selecting a card with a multiple of 4 or 6 = n(E)/n(S) = 10/30 = 1/3 (ii) From numbers 1 to 30, there are 2 numbers which are multiple of 3 and 5 i.e. {15, 30} Favorable number of events = n(E) = 2 Probability of selecting a card with a multiple of 3 and 5 = n(E)/n(S) = 2/30 = 1/15 (iii) From numbers 1 to 30, there are 14 numbers which are multiple of 3 or 5 i.e. {3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30} Favorable number of events = n(E) = 14 Probability of selecting a card with a multiple of 3 or 5 = n(E)/n(S) = 14/30 = 7/15

Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is:(i) a multiple of 4 or 6 (ii) a multiple of 3 and 5 (iii) a multiple of 3 or 5

Answer»

There are 30 cards from which one card is drawn .

Total number of elementary events = n(S) = 30

(i) From numbers 1 to 30, there are 10 numbers which are multiple of 4 or 6 i.e. {4, 6, 8, 12, 16, 18, 20, 24, 28, 30}

Favorable number of events = n(E) = 10

Probability of selecting a card with a multiple of 4 or 6 = n(E)/n(S) = 10/30 = 1/3

(ii) From numbers 1 to 30, there are 2 numbers which are multiple of 3 and 5 i.e. {15, 30}

Favorable number of events = n(E) = 2

Probability of selecting a card with a multiple of 3 and 5 = n(E)/n(S) = 2/30 = 1/15

(iii) From numbers 1 to 30, there are 14 numbers which are multiple of 3 or 5 i.e. {3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30}

Favorable number of events = n(E) = 14

Probability of selecting a card with a multiple of 3 or 5 = n(E)/n(S) = 14/30 = 7/15