Question

A box contains some cards numbered from 3 to 50. A card is drawn at random from the

box. Find the probability that the card drawn is (i) a perfect square (ii) a perfect cube.​

Answer 1

The probability of getting a card

(i) A perfect square:$\bf P(S) = \frac{1}{8}$

(ii) A perfect cube:$\bf P(C) = \frac{1}{24}$

Given:

• A box contains some cards numbered from 3 to 50.
• A card is drawn at random from the box.

To find:

• Find the probability that the card drawn is (i) a perfect square (ii) a perfect cube.

Solution:

Formula to be used:

Probability of an event: Favourable outcomes/Total outcomes

Step 1:

Find the Probability of getting a card which is a perfect square:

Total number of cards: 48

Perfect square cards are: 4,9,16,25,36,49

Favourable outcomes for perfect square cards :6

Let the event of getting a card which is a perfect square is S.

Then,

$P(S) = \frac{6}{48}$

or

$P(S) = \frac{1}{8}$

Step 2:

Find the Probability of getting a card which is a perfect cube:

Total number of cards: 48

Perfect cube cards are: 8,27

Favourable outcomes for perfect cube cards: 2

Let the event of getting a card which is a perfect cube is C.

Then,

$P(C) = \frac{2}{48}$

or

$\bf P(C) = \frac{1}{24}$

_____________________________

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Answer 2

Given,

A box contains cards numbered from 3 to 50.

To find,

The probability that the card drawn is (i) a perfect square (ii) a perfect cube.

Solution,

The probability that the card drawn is a perfect square will be 1/8 and that of a perfect cube will be 1/24.

We can easily solve this problem by following the given steps.

According to the question,

Cards = 3,4,5,6,---, 50

So, the total number of cards will be 48.

Now, to find the probability of a card having a perfect square number and a perfect cube number we will have to find the total cards having perfect squares and cubes.

Perfect square numbers = 4, 9, 16, 25, 36, 49

Perfect cube numbers = 8, 27

Then, the total numbers of perfect square cards = 5

The total numbers of perfect cube cards = 2

Now, we know,

Probability = Number of favourable outcomes/total number of outcomes

(1) Probability of a card having a perfect square number, P(S)

P(S) = Number of perfect square cards/total number of cards

P(S) = 6/48

P(S) = 1/8 [Dividing both the numbers by 6]

(2) Probability of a card having a perfect cube number, P(C)

P(C) = Number of perfect cube cards/total number of cards

P(C) = 2/48

P(C) = 1/24

Hence, the probability that the card drawn is a perfect square is 1/8 and that of a perfect cube is 1/24.