Question

A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is :

• A. $\frac{5}{44}$
• B. $\frac{1}{9}$
• C. $\frac{1}{11}$
• D. $\frac{7}{45}$

Answer 1

The Correct Option is B

Step 1: Understanding the problem:
We are given a box with cards numbered from 6 to 50. A card is drawn at random, and we need to find the probability that the drawn card has a number that is a perfect square.

Step 2: Identifying the perfect squares between 6 and 50:
A perfect square is a number that can be expressed as \(n^2\), where \(n\) is an integer. We need to find all the perfect squares between 6 and 50.
The perfect squares less than 50 are:
\[ 1^2 = 1, \, 2^2 = 4, \, 3^2 = 9, \, 4^2 = 16, \, 5^2 = 25, \, 6^2 = 36, \, 7^2 = 49 \] However, the numbers must be between 6 and 50, so we exclude 1 and 4.
The perfect squares between 6 and 50 are: \(9, 16, 25, 36, 49\).

Step 3: Total number of possible outcomes:
The total number of possible outcomes is the number of cards, which are numbered from 6 to 50. The total number of cards is: \[ 50 - 6 + 1 = 45 \]

Step 4: Number of favorable outcomes:
The favorable outcomes are the cards with perfect square numbers. From the previous step, we know that the favorable outcomes are \(9, 16, 25, 36, 49\), which are 5 numbers.

Step 5: Calculating the probability:
The probability of drawing a card with a perfect square number is the ratio of favorable outcomes to total outcomes: \[ P(\text{perfect square}) = \frac{5}{45} = \frac{1}{9} \]

Step 6: Conclusion:
The probability that the drawn card has a number which is a perfect square is \(\frac{1}{9}\).