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Find the probability of a number which is divisible by either 5 or 3 out of first 500 natural Odd Numbers.
- a)0.47
- b)0.35
- c)0.27
- d)0.58
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Find the probability of a number which is divisible by either 5 or 3 o...
The First 500 Natural Odd numbers are given as 1,3,5,7,…………….999.
The Numbers divisible by 3 from the above list are given as 3,9,15,21…………999
The above series is in Arithmetic progression,
Tn = a+(n−1)d
999 = 3+(n3−1)6 ⇒ n3 = 167
So total Numbers which are divisible by 3 in the given list is, n3 = 167
The Numbers divisible by 5 from the above list are given as 55,15,25,35…………99
The above series is in Arithmetic progression,
Tn = a+(n−1)d
995 = 5+(n5−1)10 ⇒ n5 = 100
So total Numbers which are divisible by 5 in the given list is, n3 = 100.
The Numbers divisible by 15 from the above list are given as 15,45,75,105…………975
The above series is in Arithmetic progression,
Tn = a+(n−1)d
975 = 15+(n15−1)30 ⇒ n15 = 33
So total Numbers which are divisible by 3 in the given list is, n3 = 33
So Required Probability p = p(n3)+p(n5)−p(n15) = 
= 0.468
= 0.468Most Upvoted Answer
Find the probability of a number which is divisible by either 5 or 3 o...
Probability of a number divisible by either 5 or 3 out of the first 500 natural Odd Numbers
To find the probability of a number divisible by either 5 or 3 out of the first 500 natural odd numbers, we need to determine the count of numbers that are divisible by either 5 or 3, and then divide it by the total count of numbers.
Count of numbers divisible by 5:
To find the count of numbers divisible by 5, we need to divide the last number divisible by 5 (which is less than or equal to 500) by 5.
The last number divisible by 5 is 495 (5 * 99), so the count of numbers divisible by 5 is 99.
Count of numbers divisible by 3:
To find the count of numbers divisible by 3, we need to divide the last number divisible by 3 (which is less than or equal to 500) by 3.
The last number divisible by 3 is 495 (3 * 165), so the count of numbers divisible by 3 is 165.
Count of numbers divisible by both 5 and 3 (i.e., divisible by 15):
To find the count of numbers divisible by both 5 and 3, we need to divide the last number divisible by 15 (which is less than or equal to 500) by 15.
The last number divisible by 15 is 495 (15 * 33), so the count of numbers divisible by both 5 and 3 is 33.
Count of numbers divisible by either 5 or 3:
To find the count of numbers divisible by either 5 or 3, we need to add the count of numbers divisible by 5 and the count of numbers divisible by 3, and then subtract the count of numbers divisible by both 5 and 3.
Count of numbers divisible by either 5 or 3 = Count of numbers divisible by 5 + Count of numbers divisible by 3 - Count of numbers divisible by both 5 and 3
= 99 + 165 - 33
= 231
Probability:
The total count of numbers in the given range (first 500 natural odd numbers) can be calculated by dividing the range by 2 (since it's the count of odd numbers), so the total count is 500/2 = 250.
The probability of a number being divisible by either 5 or 3 is the count of numbers divisible by either 5 or 3 divided by the total count of numbers.
Probability = Count of numbers divisible by either 5 or 3 / Total count of numbers
= 231 / 250
≈ 0.924
Rounding to two decimal places, the probability is approximately 0.92, which is not one of the given options.
Therefore, the correct answer is not among the options provided.
To find the probability of a number divisible by either 5 or 3 out of the first 500 natural odd numbers, we need to determine the count of numbers that are divisible by either 5 or 3, and then divide it by the total count of numbers.
Count of numbers divisible by 5:
To find the count of numbers divisible by 5, we need to divide the last number divisible by 5 (which is less than or equal to 500) by 5.
The last number divisible by 5 is 495 (5 * 99), so the count of numbers divisible by 5 is 99.
Count of numbers divisible by 3:
To find the count of numbers divisible by 3, we need to divide the last number divisible by 3 (which is less than or equal to 500) by 3.
The last number divisible by 3 is 495 (3 * 165), so the count of numbers divisible by 3 is 165.
Count of numbers divisible by both 5 and 3 (i.e., divisible by 15):
To find the count of numbers divisible by both 5 and 3, we need to divide the last number divisible by 15 (which is less than or equal to 500) by 15.
The last number divisible by 15 is 495 (15 * 33), so the count of numbers divisible by both 5 and 3 is 33.
Count of numbers divisible by either 5 or 3:
To find the count of numbers divisible by either 5 or 3, we need to add the count of numbers divisible by 5 and the count of numbers divisible by 3, and then subtract the count of numbers divisible by both 5 and 3.
Count of numbers divisible by either 5 or 3 = Count of numbers divisible by 5 + Count of numbers divisible by 3 - Count of numbers divisible by both 5 and 3
= 99 + 165 - 33
= 231
Probability:
The total count of numbers in the given range (first 500 natural odd numbers) can be calculated by dividing the range by 2 (since it's the count of odd numbers), so the total count is 500/2 = 250.
The probability of a number being divisible by either 5 or 3 is the count of numbers divisible by either 5 or 3 divided by the total count of numbers.
Probability = Count of numbers divisible by either 5 or 3 / Total count of numbers
= 231 / 250
≈ 0.924
Rounding to two decimal places, the probability is approximately 0.92, which is not one of the given options.
Therefore, the correct answer is not among the options provided.
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Find the probability of a number which is divisible by either 5 or 3 out of first 500 natural Odd Numbers.a)0.47b)0.35c)0.27d)0.58Correct answer is option 'A'. Can you explain this answer?
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