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Q.

Cards marked with numbers 13, 14, 15, ……., 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the card drawn is

(i) divisible by 5 and
(ii) a number is a perfect square

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a

\frac{5}{4}

and

\frac{1}{4}

b

\frac{3}{24}

and

\frac{2}{3}

c

\frac{5}{24}

and

\frac{1}{12}

d

\frac{1}{24}

and

\frac{1}{24}

answer is C.

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Detailed Solution

Given,
Cards marked with numbers 13, 14, 15, ……., 60.
Total cards which marked with number divisible by 5 from 13 to 60 are,
15, 20, 25, 30, 35, 40, 45, 50, 55, 60
So, total favorable results = 10
Total possible results = 48 (60-12)
So, required probability for first case,

P_{1} = \frac{(Number of favorable results)}{(Total number of possible results)}

P_{1} = \frac{10}{48}

P_{1} = \frac{5}{24}

(ii) Card with a perfect square number are 16, 25, 36 and 49
Total number exact square from 13 to 60 = 4
So, Probability

for second case,

P_{2} = \frac{(Number of favorable results)}{(Total number of possible results)}

P_{2} = \frac{4}{48}

P_{2} = \frac{1}{12}

Option 3 is correct.

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