Q23 of 34 Page 1

Cards marked with numbers 1, 3, 5… 49 are placed in a box and mixed thoroughly. One card is drawn from the box. Find the probability that the number on the card is

divisible by 3

As the numbers of cards in an AP, with first term a = 1 and common difference d = 2


Let the no of cards be 'n'


Number on nth card = 49


⇒ a + (n - 1)d = 49 [As nth term of an AP = a + (n - 1)d ]


⇒ 1 + (n - 1)2 = 49


⇒ (n - 1)2 = 48


⇒ n - 1 = 24


⇒ n = 25


Total No of cards = 25


Cards having no's divisible by 3 = {3, 9, 15, 21, 27, 33, 39, 45}


No of cards having no's divisible by 3 = 8


We know that,


Probability of an event


⇒ Probability of getting a card having a number divisible by 3




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