oal Fhts: T06 points Total Grade Points: 5 grade points. Probability of an even
ID: 3370732 • Letter: O
Question
oal Fhts: T06 points Total Grade Points: 5 grade points. Probability of an even integer 1, (16%) Consider 3 digits integers 100 till 999. (a) (6%) Compute the probability of 3 digits even number such as 100, 102, 104, etc (b) (10%) Compute the probability of a 3 digits integers with the sum of3 digits an even integer. For example, 6) but ? 15 is 3 digits with sum of 3 digits odd (sum-9). 125 is 3 digits with sum of 3 digits even (sum (2490) Even integer continued. 2, until 100! (here n! is (a) (8%) Compute the probability of an even integer among the 100 integers 1 !, 2! 31, n factorial or n* (n-1)* (n-2) *... 1) , (b) (16%) Compute the probability of an even integer among the 100 integers: 1, 1+2, 1+2+3, 1+2+3+4, 1+2+3+... +99, and 1+2+3+... +100Explanation / Answer
Question 1:
From 100 till 999, there are 900 three digit numbers.
a) Out of the total 900 integers, 450 are even and 450 are odd.
Therefore the probability that the three digit number is even is computed as:
= 450 / 900
= 0.5
Therefore 0.5 is the required probability here.
b) 100: Sum of digits is odd
101: Sum of digits is even
102: odd
103: even
104: odd and so on.....
Therefore for half of the numbers the sum of digits would be even and for other half it would be odd. Therefore the required probability here would also be 0.5
Therefore 0.5 is the required probability here.
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