Understanding the Probability Problem
We need to find the probability of drawing a card that shows a perfect square number. The cards are numbered sequentially from 33 to 92.
Calculating Total Possible Outcomes
First, determine the total number of cards in the bag. This is the count of numbers from 33 to 92, inclusive.
Total numbers = (Last Number - First Number) + 1
Total numbers = (92 - 33) + 1 = 59 + 1 = 60
So, there are 60 possible outcomes when drawing one card.
Identifying Favorable Outcomes (Perfect Squares)
Next, identify the numbers between 33 and 92 (inclusive) that are perfect squares.
- We look for squares of integers: $n^2$.
- $5^2 = 25$ (less than 33)
- $6^2 = 36$ (within the range 33-92)
- $7^2 = 49$ (within the range 33-92)
- $8^2 = 64$ (within the range 33-92)
- $9^2 = 81$ (within the range 33-92)
- $10^2 = 100$ (greater than 92)
The perfect squares between 33 and 92 are 36, 49, 64, and 81.
There are 4 favorable outcomes.
Calculating the Probability
The probability of an event is calculated as:
P(Event) = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
In this case, the event is drawing a perfect square card.
P(Perfect Square) = $\frac{4}{60}$
Simplify the fraction:
P(Perfect Square) = $\frac{4 \div 4}{60 \div 4} = \frac{1}{15}$
Conclusion
The probability that the number on the drawn card is a perfect square is $\frac{1}{15}$.
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Important Questions from Probability
The probability of being 53 Sundays in year 2020 is-
Three dice are thrown randomly. The probability of coming 3 in at least one die is
The probability of having 53 Tuesdays in an ordinary year is:
Two dice are thrown simultaneously The probability of getting the sum 2 or 8 or 12 is
If two balanced dice are tossed once, the probability of the event, that the sum of the integers coming on the upper sides of the two dice is 9, is
