18) The probability that a number selected at random from 1 to 100 is ...
Probability of selecting a multiple of 5 or 6 from 1 to 100
To find the probability of selecting a multiple of 5 or 6 from 1 to 100, we need to first find the number of multiples of 5 or 6 in this range. We can then divide this number by the total number of integers in the range (which is 100).
Number of multiples of 5 in the range
The multiples of 5 in the range 1 to 100 are:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100
So, there are 20 multiples of 5 in the range.
Number of multiples of 6 in the range
The multiples of 6 in the range 1 to 100 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96
So, there are 16 multiples of 6 in the range.
Number of multiples of both 5 and 6 in the range
The multiples of both 5 and 6 in the range 1 to 100 are:
30, 60, 90
So, there are 3 multiples of both 5 and 6 in the range.
Total number of multiples of 5 or 6 in the range
To find the total number of multiples of 5 or 6 in the range, we need to add the number of multiples of 5 and 6, and then subtract the number of multiples of both 5 and 6 (to avoid counting them twice).
Total number of multiples of 5 or 6 = (20 + 16) - 3 = 33
Probability of selecting a multiple of 5 or 6
Since there are 33 multiples of 5 or 6 in the range, and the total number of integers in the range is 100, the probability of selecting a multiple of 5 or 6 at random is:
33/100 = 0.33
Answer
Therefore, the answer is (b) 0.33.