An integer is chosen between 0 and 100.

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An integer is chosen between 0 and 100. What is the probability that it is
(i) divisible by 7?
(ii) not divisible by 7?

Solution:

Integers between 0 and 100 = 99
(i) Number divisible by 7 are
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98 = 14
Probability = \\ \frac { 14 }{ 99 }
(ii) Not divisible by 7 are 99 – 14 = 85
Probability = \\ \frac { 85 }{ 99 }

Cards marked with numbers 1, 2, 3, 4, 20 are well shuffled and a card is drawn at random.
What is the probability that the number on the card is
(i) a prime number
(ii) divisible by 3
(iii) a perfect square? (2010)

Solution:

Number cards is drawn from 1 to 20 = 20
One card is drawn at random
No. of total (possible) events = 20
(i) The card has a prime number
The prime number from 1 to 20 are 2, 3, 5, 7, 11, 13, 17, 19
Actual No. of events = 8
P(E) = \frac { Number\quad of\quad actual\quad events }{ Number\quad of\quad total\quad events }
= \\ \frac { 8 }{ 20 }
= \\ \frac { 2 }{ 5 }
(ii) Numbers divisible by 3 are 3, 6, 9, 12, 15, 18
No. of actual events = 6
P(E) = \frac { Number\quad of\quad actual\quad events }{ Number\quad of\quad total\quad events }
= \\ \frac { 6 }{ 20 }
= \\ \frac { 3 }{ 10 }
(iii) Numbers which are perfect squares = 1, 4, 9, 16 = 4
P(E) = \frac { Number\quad of\quad actual\quad events }{ Number\quad of\quad total\quad events }
= \\ \frac { 4 }{ 20 }
= \\ \frac { 1 }{ 5 }

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