Question

A box contains cards with numbers marked from 1 to 100. Find the probability of getting a card

(a) with a perfect square (b) Divisible by both 25 and 50

• A. a) $\frac{1}{10}$ b) $\frac{1}{50}$
• B. a) $\frac{1}{5}$ b) $\frac{1}{25}$
• C. a) $\frac{1}{2}$ b) $\frac{1}{5}$
• D. a) $\frac{1}{4}$ b) $\frac{1}{100}$

Answer 1

The correct option is A

a) $\frac{1}{10}$ b) $\frac{1}{50}$

There are 100 cards .

Hence the number of total outcomes = 100

(a) with a perfect square

There are 10 cards with perfect square. i.e Favourable outcomes are {1 , 4 ,9 ,16, 25,36,49 , 64 ,81 , 100}

Hence P( with a perfect square ) = $\frac{FavourableOutcomes}{Numberoftotaloutcomes}$

= $\frac{10}{100}$

= $\frac{1}{10}$

(b) Divisible by both 25 and 50

There are only 2 numbers which are divisible by both 25 and 50 , i.e 50 and 100

Hence number of favourable outcome = 2

Hence P ( divisible by both 25 and 50 ) = $\frac{Numberoffavourableoutcome}{Totalnumberofoutcomes}$

= $\frac{2}{100}$

= $\frac{1}{50}$