Question

A box contains cards, number 1 to 90. A card is drawn at random from the box. Find the probability that the selected card bears



a.(i) two digit number (ii) perfect square number

Answer 1

Sample space = {1,2,3,4,5,6,7,8,.......90}

(i) Two digit number

Outcomes of two digit number = 80

Therefore

Probability = 80/90

= 8/9


(ii) a perfect square

Outcomes = {4,9,16,25,36,49,64}

Therefore

Probability = 7/80

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Answer 2

i) The  probability that the selected card bears a two digit number is 0.9.

ii) The probability that the selected card bears a perfect square is 0.1.

Explanation:

Given : A box contains cards, number 1 to 90.

A card is drawn at random from the box.

Total outcomes = 90

a) two digit numbers from 1 to 90= 10 , 11 , 12, .... , 90 = 90-9=81

i.e.  Favorable outcomes = 81

So , the probability that the selected card bears a two digit number= $\dfrac{Favorable\ outcomes}{Total\ outcomes}$

$=\dfrac{81}{90}=\dfrac{9}{10}=0.9$

∴ The  probability that the selected card bears a two digit number is 0.9.

b) Perfect square numbers from 1 to 90= 1, 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 .

i.e. Favorable outcomes = 9

Now , the probability that the selected card bears a perfect square = $\dfrac{Favorable\ outcomes}{Total\ outcomes}$

$=\dfrac{9}{90}=\dfrac{1}{10}=0.1$

Therefore , the probability that the selected card bears a perfect square is 0.1.

#Learn more :

Cards marked with numbers 3, 4, 5, ..............., 50 are placed in a bag and mixed thoroughly. One card is drawn at random from the bag. Find the probability that number on the card drawn is:

a. Divisibleby7.

b. Aperfectsquare.

c. A multiple of 6

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