Question

A box contains cards numbered 3 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect cube, is a) 1/48 b) 1/24 c) 2/47 d)
1/16​

Answer 1

Answer:

Option B is the correct

Explanation:-

Total no.of perfect cubes in 3 to 50 is 6

therefore 6×4 =24

option B is 1/24

Answer 2

The probability that the drawn card has a number which is a perfect cube is 1/24

Given:

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

To Find:

The probability that the drawn card has a number which is a perfect cube

Solution:

• Probability of an event  = n(E)/n(S)  
• n(E) = number of possible outcome of event
• n(S) = number of possible sample space outcome

Step 1:

Sample space is cards from 3 to 50

S= { 3 , 4 ,  ... , 49 , 50 }

n(S) = 48

Step 2:

Assume That E is the event of Getting perfect cube from 3 to 50

E = { 8 , 27 }

n(E) = 2

Step 3:

Find the probability that the drawn card has a number which is a perfect cube

P(E) =n(E)/n(S)

P(E) = 2/48

P(E) = 1/24

Hence, The probability that the drawn card has a number which is a perfect cube is 1/24

Correct option is b) 1/24