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: Understand the problem:
We are given a box that contains cards numbered from 6 to 50, and we are asked to find the probability that the number on a randomly drawn card is a perfect square.

Step 2: Identify the total number of cards:
The cards are numbered from 6 to 50, so the total number of cards is:
\[ 50 - 6 + 1 = 45 \] Thus, there are 45 cards in total.

Step 3: Identify the perfect squares between 6 and 50:
The perfect squares between 6 and 50 are the squares of integers, starting from the smallest integer whose square is greater than or equal to 6, up to the largest integer whose square is less than or equal to 50. These integers are:
\[ \sqrt{6} \approx 2.45 \quad \text{and} \quad \sqrt{50} \approx 7.07 \] So, the integers whose squares fall between 6 and 50 are 3, 4, 5, 6, and 7. The corresponding perfect squares are:
\[ 3^2 = 9, \, 4^2 = 16, \, 5^2 = 25, \, 6^2 = 36, \, 7^2 = 49 \] Thus, the perfect squares between 6 and 50 are \( 9, 16, 25, 36, 49 \). There are 5 such numbers.

Step 4: Calculate the probability:
The probability is the ratio of favorable outcomes (i.e., the number of perfect squares) to the total number of outcomes (i.e., the total number of cards). Thus, the probability is:
\[ P(\text{perfect square}) = \frac{5}{45} = \frac{1}{9} \]

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