Alice and Bob each picks an integer number uniformly at random between 1 and n. Assume that all possible combinations of two numbers are equally likely to be picked. What is the probability that Alice’s number is bigger than Bob’s?

The answer is 1/n

Step-by-step explanation:

First number = Alice's number

Second Number = Bob's Number

There are already 2 good answers if the first number is AT LEAST 1 greater than the second.

However, what if the first number is EXACTLY 1 greater than the second?

I will assume the first number is removed from the array after being selected.

If the first number is 1, then it is impossible, because the second number cannot be less than 1.

If the first number is 2, then the second number could be 1, which has a probability of 1/(n-1)

If the first number is 3, then the second number could be 2, which has a probability of 1/(n-1)

etc…

There is a 1/n probability of each first number selected, so the answer would be:

0*1/n+1/n*1/(n−1)+1/n*1/(n−1)+⋯+1/n*1/(n−1)

There are n terms in that series.

That gives us:

0+1/n(n−1)+1/n(n−1)+⋯+1/n(n−1)

There are n-1 of those identical terms, because 1 of the terms is 0.

(n−1)/n(n−1)=1/n

So the answer is 1/n.

fdvs

step-by-step explanation: vsfdvsfvd

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk