Nevernevergiveup wrote:
If four fair dice are thrown simultaneously, what is the probability of getting at least one pair?
(A) 1/6
(B) 5/18
(C) 1/2
(D) 2/3
(E) 13/18
We want P(get at least 1 pair)
When it comes to probability questions involving
"at least," it's typically best to use the
complement.
That is, P(Event A happening) = 1 - P(Event A
not happening)
So, here we get: P(getting at least 1 pair) = 1 -
P(not getting at least 1 pair)What does it mean to
not get at least 1 pair? It means getting zero pairs.
So, we can write: P(getting at least 1 pair) = 1 -
P(getting zero pairs)P(getting zero pairs)P(getting zero pairs)= P(ANY value on 1st die
AND different value on 2nd die
AND different value on 3rd die
AND different value on 4th die)
= P(ANY value on 1st die)
x P(different value on 2nd die)
x P(different value on 3rd die)
x P(different value on 4th die)
= 1
x 5/6
x 4/6
x 3/6
=
5/18 So, P(getting at least 1 pair) = 1 -
5/18 = 13/18
Answer: E
Cheers,
Brent
_________________