The question on an examination paper are numbered from 1 to 50. A question is chosen at random.?

Write down,giving each answer as a fraction in its simplest form, the probability that the number of the question chosen will


(a) contain more than a single digit,


(b) be a perfect square,


(c) contain at least one figure 3,


(d) not be divisible by either 2 or 3.


Do explain to me in details how.


THANKS

The question on an examination paper are numbered from 1 to 50. A question is chosen at random.?
a) numbers from 10 to 50 are those that have more than one digit, there are 50-10+1= 41 such numbers so the probability is 41/50.





b)1=1^2 up to 49=7^2 are all the perfect squares. There are 7. Probability 7/50.





c)It could be 03,13, 23, 33 or 43 so the probability is 5/50=1/10. (in fact that would be true with any number that ended in 0)





d)50/2 = 25 so there are 25 numbers divisible by 2.


50/3 = 16.6... so there are 16 that are divisible by 3.


50/6 = 8.33... (divide by 6 = least common multiple of 2 and 3, to calculate how many numbers are divisible by both 2 and 3) so the two previous sets 8 elements in common.





Then the numbers that are not divisible neither by 2 nor 3 are 50 - 25 - 16 + 8 = 17 (Losing time counting all those numbers woudn't be very helpful in an exam). Then the probability is 17/50








I hope that helps.
Reply:P (More than 1 digit) = 41/50 (all numbers besides 1-9)








Perfect square = any number that can be written as n^2 for some integers... any number that has a round square root





1, 4, 9, 16, 25, 36, 49





P (Perfect Square) = 7/50








At least one 3:





At least one digit is 3, but you have to also include the 30s:





3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43





P (Contains at least one 3) = 14/50





Not Divisible by 2 or 3:





Each number has to not be able to be divided by 2 or 3 to get an even number:





1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49





So, P(Not divisible by 2 or 3) = 17/50
Reply:a. 41/50 (simple, 41 numbers that contain more than 1 digit)





b. perfect squares:1, 4, 9, 16, 25, 36, 49


thus 7/50 (7 perfect squares)





c. 14/50=7/25 (14 integers that contain 3)





d. I dont understand but if integers are not divisible by 2 AND 3 then there are 25 not divisible by 2 and of those 25 17 are not divisible by 3 and 2. thus 17/50 probability.
Reply:(a) How many numbers between 1 and 50 contain more than one digit? 41 of them . So the chances of picking a number with more than one digit is 41/50.





(b)There are 7 perfect squares between 1 and 50, so the probability of picking one is 7/50.





You figure out the rest yourself I'm sure