Finding the Probability of Drawing a Perfect Square

Oct 13, 2025 by thesweetdesigns.com 61 views

**A Bag Contains Cards Which Are Numbered from 5 to 100 Such That Each Card Bears a Different Number. A Card is Drawn at Random. Find the Probability that Number on the Card is (i) a Perfect Square (ii) a 2-digit Number**

In this article, we will discuss the concept of probability and how to find the probability of drawing a card with a specific number from a bag containing cards numbered from 5 to 100.

What is Probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1 that represents the chance or probability of an event happening. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.

Finding the Probability of Drawing a Perfect Square

To find the probability of drawing a perfect square, we need to first identify the perfect squares between 5 and 100.

Perfect Squares between 5 and 100

The perfect squares between 5 and 100 are:

9 (3^2)
16 (4^2)
25 (5^2)
36 (6^2)
49 (7^2)
64 (8^2)
81 (9^2)

There are 7 perfect squares between 5 and 100.

Total Number of Cards

The total number of cards in the bag is 96 (100 - 5 + 1).

Probability of Drawing a Perfect Square

The probability of drawing a perfect square is the number of perfect squares divided by the total number of cards.

Probability = Number of perfect squares / Total number of cards = 7 / 96 = 0.0729 (or 7.29%)

Therefore, the probability of drawing a perfect square from the bag is 7.29%.

Finding the Probability of Drawing a 2-digit Number

To find the probability of drawing a 2-digit number, we need to first identify the 2-digit numbers between 5 and 100.

2-digit Numbers between 5 and 100

The 2-digit numbers between 5 and 100 are:

There are 90 2-digit numbers between 5 and 100.

Probability of Drawing a 2-digit Number

The probability of drawing a 2-digit number is the number of 2-digit numbers divided by the total number of cards.

Probability = Number of 2-digit numbers / Total number of cards = 90 / 96 = 0.9375 (or 93.75%)

Therefore, the probability of drawing a 2-digit number from the bag is 93.75%.

Q: What is the probability of drawing a perfect square from the bag? A: The probability of drawing a perfect square from the bag is 7.29%.

Q: What is the probability of drawing a 2-digit number from the bag? A: The probability of drawing a 2-digit number from the bag is 93.75%.

Q: How many perfect squares are there between 5 and 100? A: There are 7 perfect squares between 5 and 100.

Q: How many 2-digit numbers are there between 5 and 100? A: There are 90 2-digit numbers between 5 and 100.

Q: What is the total number of cards in the bag? A: The total number of cards in the bag is 96.

In this article, we discussed the concept of probability and how to find the probability of drawing a card with a specific number from a bag containing cards numbered from 5 to 100. We also found the probability of drawing a perfect square and a 2-digit number from the bag.