Question

What is the probability of choosing a pair that contains ONLY cards labeled with the letters B, C, or F?

Answer 1

`Pr = (1)/(6)`

Explanation:

Given

`Cards = \{A,B,C,D,E,F\}`

`r = 2` --- selection

Required

Probability of choosing a pair with only B, C and F

The total selection is: 36

This is calculated as thus:

`First = 6` --- First selection can be any of the 6 cards

`Second = 6` --- Second selection can be any of the 6 cards [No restriction]

So, we have:

`n = First * Second`

`n = 6 * 6`

`n = 36`

The pair of only B, C or F is:

`Pair = \{(B,C), (B,F), (C,B),(C,F),(F,B),(F,C)\}`

`n(Pair) = 6`

So, the probability is:

`Pr = (n(Pair))/(n)`

`Pr = (6)/(36)`

Simplify

`Pr = (1)/(6)`