8. Consider the set of all the 2-digit integers, S 10, 11, 12,, 98, 99) ) O poin
ID: 3920820 • Letter: 8
Question
8. Consider the set of all the 2-digit integers, S 10, 11, 12,, 98, 99) ) O points) How many numbers arethere ls S7 (b) (3 points) Randomly choose a number in S. What is the probability that this number is divisible by 7 (c) (3 points) You wish to type all these numbers. How many times do you have to hit the key for 0? (d) (3 points) You wish to type all these numbers. How many times do you have to hit the key for 5? (e) (3 points) You wish to type all these numbers but the key for 2 is broken. How many num- bers are affected?Explanation / Answer
S = {10, 11, 12, .., 98, 99}
a) How many numbers are there is S?
since, S contains all continous numbers.
Numbers in S = highest number - lowest number + 1 = 99 -10 + 1 = 90
b)Randmly chose a number in S. What is it's probability that it is divisible by 7.
To find out the probability, we need to find out how many numbers are divisible by 7 in S.
these are 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.
So probablity = no. of favourable cases / no. of all cases = 13/90
c) How many times we must have to hit 0, to type all numbers.
we get 0, at all multiples of 10.
these are 10, 20, 30, ... 90.
so the answer is : 9
d) How many times we must have to hit 0, to type all numbers.
we get 5 in 15, 25, 35, ...., 95(total 9)
along with these numbers from 50 to 59, also contains 5.(total 10)
so the answer is 19.
e)if number 2 key is broken, then how many numbers will be affected.?
To find this, we need to find, how many numbers contain digit 2.
To do this, we can follow the concept used in part d.
we get 2 in 12,22,32,42, 52, 62, 72, 82, 92.(total 9)
Along with these 2 comes in 20 to 29, 10 numbers but we have considered 22 already.
So, the final answer is: 9 +10 - 1 = 18.
If there is anything that you do not understand, then please mention it in the comments section.
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