Question

"cards are marked with number 5 to 100 are placed in a box and mixed thoroughly one card is drawn from the box find the probability that the number on the card is.

a)a perfect square.
b)a multiple of 7
c)prime number less than 50."

Answer 1

The probabilities are calculated by identifying the number of favorable outcomes that fit each condition (perfect square, multiple of 7, prime number less than 50) and dividing by the total possible outcomes, which are cards numbered 5 to 100.

Step-by-step explanation:

Probability of Drawing Specific Cards

Let us consider each of the parts of the question separately, involving a box with cards numbered from 5 to 100:

1. Perfect Square: The perfect squares between 5 and 100 are 9, 16, 25, 36, 49, 64, 81, and 100. That means there are 8 perfect squares. Since there are 96 possible numbers (100 - 5 + 1 = 96), the probability is 8/96 or 1/12.
2. Multiple of 7: The multiples of 7 between 5 and 100 are 7, 14, 21, ..., 98. There are 14 multiples of 7 within this range. So, the probability is 14/96 or 7/48.
3. Prime Number Less Than 50: The prime numbers between 5 and 50 are 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. There are 13 such prime numbers. The probability is thus 13/96.

We calculated the probability for each specific condition by counting the favorable outcomes and dividing by the total number of possible outcomes.