Three numbers are chosen at random without replacement from {1, 2, 3, ...... 8}. The probability that their minimum is 3, given that their maximum is 6, is (1) `3/8` (2) `1/5` (3) `1/4` (4) `2/5`

Options

A. `3/8`
B. `1/5`
C. `1/4`
D. `2/5`

Answer

B

Explanation

Given set of numbers is `{1,2,3,4,5,6,7,8}`
We have to select three numbers
Let us assume that
event A `to` inselected three numbers minimum is 3
event B `to` in selected three numbers maximum is 6
We have to find P (A/B).
`P(A//B)=(P(AnnB))/(P(B))=(n(AnnB))/(N(B))`
`AnnB` = in selected three numbers, minimum is 3 and maximum is 6
`therefore` The remaining number is either 4 or 5
`therefore n(AnnB)=2`
n(B) = selecting two numbers from `1,2,3,4,5` (as maximum of numbers is 6)
`=""^(5)C_(2)`
`thereforeP(A//B)=(n(AnnB))/(n(B))=(2)/(""^(5)C_(2))=1/5`