1.

From 25 identical cards, numbered 1, 2, 3, 4, 5, ……, 24, 25: one card is drawn at random. Find the probability that the number on the card drawn is a multiple of:(i) 3 (ii) 5 (iii) 3 and 5 (iv) 3 or 5

Answer»

There are 25 cards from which one card is drawn.

Total number of elementary events = n(S) = 25

(i) From number 1 to 25, there are 8 number which are multiple of 3 i.e. {3, 6, 9, 12, 15, 18, 21, 24}, 

Favorable number of events = n(E) = 8

Probability of selecting a card with a multiple of 3 = n(E)/n(S) = 8/25

(ii) From number 1 to 25, there are 5 number which are multiple of 5 i.e. {5, 10, 15, 20, 25}

Favorable number of events = n(E) = 5

Probability of selecting a card with a multiple of 5 = n(E)/n(S) = 5/25 = 1/5

(iii) From number 1 to 25, there is one number which are multiple of 3 and 5 i.e. {15}

Favorable number of events = n(E) = 1

Probability of selecting a card with a multiple of 3 and 5 = n(E)/n(S) = 1/25 

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

Favorable number of events = n(E) = 12

Probability of selecting a card with a multiple of 3 or 5 = n(E)/n(S) = 12/25


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