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Question

A box contains 100 cards marked with numbers 1 to 100. If one card is drawn randomly from the box. Find the probability that it bears.
(1) Even prime number.
(2) A number divisible by 7.
(3) The number at unit place is 9.

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Solution

There are 100 cards in the box marked with number 1 to 100.
A card is drawn randomly from it.
Number of possible outcomes = 100
(1) Let A be the event that the card bears an even prime number.
There is only 1 even prime number from 1 to 100, that is '2'.
The number of outcomes favourable to A is 1.
P(A)=1100=0.01
(2) Let B be the event that the card bears a number divisible by 7.
Numbers divisible by 7 from 1 to 100 are
7,14,21,28,35,42,56,63,70,77,84,91,98
There are 13 multiples of 7 from the numbers 1 to 100.
The number of outcomes favourable to B is 13.
P(A)=13100=0.13
(3) Let be the event that the card bears a number that has 9 at the unit place.
The numbers from 1 to 100 that have 9 at the units place are
9,19,29,39,49,59,69,79,89,99
There are 10 numbers that have 9 at the unit place.
The number of outcomes favourable to C is 10.
P(A)=10100=0.1

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