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Out of all the 2 - digit integers between 1 to 200, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?
- a)11/90
- b)33/90
- c)55/90
- d)77/90
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Out of all the 2 - digit integers between 1 to 200, a 2-digit number h...
There are total 90 two digit numbers, out of them 13 are divisible by 7, these are 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.
Therefore, probability that selected number is not divisible by 7 = 1 – 13/90 = 77/90.
So, option (D) is true.
Most Upvoted Answer
Out of all the 2 - digit integers between 1 to 200, a 2-digit number h...
To solve this problem, we need to determine the number of 2-digit integers between 1 and 200 that are not divisible by 7 and divide that by the total number of 2-digit integers between 1 and 200.
**Total Number of 2-Digit Integers between 1 and 200:**
There are 200 - 9 = 191 2-digit integers between 1 and 200.
**Number of 2-Digit Integers divisible by 7:**
To find the number of 2-digit integers divisible by 7, we need to find the largest and smallest 2-digit integers divisible by 7 and subtract them.
The largest 2-digit integer divisible by 7 is 196.
The smallest 2-digit integer divisible by 7 is 14.
To find the number of integers between 14 and 196, inclusive, we subtract the smallest from the largest and add 1: 196 - 14 + 1 = 183.
**Number of 2-Digit Integers not divisible by 7:**
To find the number of 2-digit integers not divisible by 7, we subtract the number of integers divisible by 7 from the total number of 2-digit integers:
191 - 183 = 8.
**Probability:**
The probability is the number of successful outcomes (2-digit integers not divisible by 7) divided by the total number of possible outcomes (2-digit integers between 1 and 200).
Probability = Number of 2-Digit Integers not divisible by 7 / Total Number of 2-Digit Integers
= 8 / 191
= 77 / 90
Therefore, the probability that the selected number is not divisible by 7 is 77/90.
Hence, the correct answer is option D) 77/90.
**Total Number of 2-Digit Integers between 1 and 200:**
There are 200 - 9 = 191 2-digit integers between 1 and 200.
**Number of 2-Digit Integers divisible by 7:**
To find the number of 2-digit integers divisible by 7, we need to find the largest and smallest 2-digit integers divisible by 7 and subtract them.
The largest 2-digit integer divisible by 7 is 196.
The smallest 2-digit integer divisible by 7 is 14.
To find the number of integers between 14 and 196, inclusive, we subtract the smallest from the largest and add 1: 196 - 14 + 1 = 183.
**Number of 2-Digit Integers not divisible by 7:**
To find the number of 2-digit integers not divisible by 7, we subtract the number of integers divisible by 7 from the total number of 2-digit integers:
191 - 183 = 8.
**Probability:**
The probability is the number of successful outcomes (2-digit integers not divisible by 7) divided by the total number of possible outcomes (2-digit integers between 1 and 200).
Probability = Number of 2-Digit Integers not divisible by 7 / Total Number of 2-Digit Integers
= 8 / 191
= 77 / 90
Therefore, the probability that the selected number is not divisible by 7 is 77/90.
Hence, the correct answer is option D) 77/90.
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Out of all the 2 - digit integers between 1 to 200, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?a)11/90b)33/90c)55/90d)77/90Correct answer is option 'D'. Can you explain this answer?
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