Question

Let x be a discrete random variable. if pr(x<6) = 1/7, and pr(x>6) = 1/4, then what is pr(x=6)?

Answer 1

`pr(x=6)=(17)/(28)`

Explanation:

Well the probabilities should all up to 1. This means pr(x<6) + pr(x=6) + pr(x>6) = 1.

So plugging in the known values we get:
`(1)/(7) + pr(x=6) + (1)/(4)=1`

To make things easier, let's multiply the 1/7 by 4/4 and 1/4 by 7/7

`(4)/(28)+pr(x=6)+(7)/(28)=1`

Now combine like terms:
`pr(x=6)+(11)/(28)=1`

Subtract 11/28 from both sides

`pr(x=6)=(17)/(28)`