A bag contains 100 identical marble stones which are numbered from 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears :
(i) a perfect square number.
(ii) a number divisible by 4.
(iii) a number divisible by 5.
(iv) a number divisible by 4 or 5.
(v) a number divisible by 4 and 5.

Question

A bag contains 100 identical marble stones which are numbered from 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears :
(i) a perfect square number.
(ii) a number divisible by 4.
(iii) a number divisible by 5.
(iv) a number divisible by 4 or 5.
(v) a number divisible by 4 and 5.

KnowledgeBoat · Accepted Answer

There are 100 identical marble stones. ∴ No. of possible outcomes = 100. (i) Stones containing a perfect square number are numbered : 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. No. of favourable outcomes = 10. P(drawing a stone with perfect square number) = . Hence, the probability of drawing a stone bearing a perfect square number = . (ii) Stones containing a number which is divisible by 4 are numbered : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100. No. of favourable outcomes = 25. P(drawing a stone with a number divisible by 4) = . Hence, the probability of drawing a stone with a number divisible by 4 = . (iii) Stones containing a number which is divisible by 5 are numbered : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100. No. of favourable outcomes = 20. P(drawing a stone with a number divisible by 5) = . Hence, the probability of drawing a stone with a number divisible by 5 = . (iv) Stones containing a number which is divisible by 4 or 5 are numbered : 4, 8, 12, 16, 24, 28, 32, 36, 44, 48, 52, 56, 64, 68, 72, 76, 84, 88, 92, 96, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100. No. of favourable outcomes = 40. P(drawing a stone with a number divisible by 4 or 5) = . Hence, the probability of drawing a stone with a number divisible by 4 or 5 = . (v) Stones containing a number which is divisible by 4 and 5 are numbered : 20, 40, 60, 80, 100. No. of favourable outcomes = 5. P(drawing a stone with a number divisible by 4 and 5) = . Hence, the probability of drawing a stone with a number divisible by 4 and 5 = .

Mathematics

Probability

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Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is :
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