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Mathematics

A game of numbers has cards marked with 11, 12, 13, ……, 40. A card is drawn at random. Find the probability that the number on the card drawn is :

(i) a perfect square.

(ii) divisible by 7.

Probability

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Answer

There are 30 cards.

∴ No. of possible outcomes = 30.

(i) Numbers that are perfect square between 11 to 40 are 16, 25, 36.

∴ No. of favourable outcomes = 3

P(that the number on the card is a perfect square)

= No. of favourable outcomesNo. of possible outcomes=330=110\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{30} = \dfrac{1}{10}.

Hence, the probability that the number on the card is a perfect square = 110\dfrac{1}{10}.

(ii) Numbers that are divisible by 7 between 11 to 40 are 14, 21, 28, 35.

∴ No. of favourable outcomes = 4

P(that the number on the card is divisible by 7)

= No. of favourable outcomesNo. of possible outcomes=430=215\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{4}{30} = \dfrac{2}{15}.

Hence, the probability that the number on the card is divisible by 7 = 215\dfrac{2}{15}.

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