SOLUTION: Amber rolls a 6-sided die. On her first roll, she gets a "4". She rolls again. (a) What is the probability that the second roll is also a "4". P(4 | 4) = (b) What is the probabi

Algebra.Com
Question 1210426: Amber rolls a 6-sided die. On her first roll, she gets a "4". She rolls again.
(a) What is the probability that the second roll is also a "4".
P(4 | 4) =
(b) What is the probability that the second roll is a "2".
P(2 / 4) =
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3822)   (Show Source): You can put this solution on YOUR website!

The answer to each question is 1/6 since there is 1 side desired out of 6 sides total.

It does not matter what the previous roll was. Each roll of the die is independent from any other.

Answer by ikleyn(52968)   (Show Source): You can put this solution on YOUR website!
.
Amber rolls a 6-sided die. On her first roll, she gets a "4". She rolls again.
(a) What is the probability that the second roll is also a "4".
P(4 | 4) =
(b) What is the probability that the second roll is a "2".
P(2 / 4) =
~~~~~~~~~~~~~~~~~~~~~~~~~~~


For both your questions, (a) and (b), the outcomes of the second roll are independent from outcomes of the first roll. 

THEREFORE,  

    in question  (a)   P(4 | 4) = 1/6,  the same as  P(4)  in the first roll and/or  P(4) in the second roll.

         To write here P(4 | 4)  is somehow awkward, if you don't want to deceive yourself and people around, 
         because the outcomes of the first roll and of the second roll are independent
         and this independence is obvious and is well known to all, to anyone and to everybody.



    in question (b)  P(2 | 4) = 1/6,  the same as  P(2)  in the first roll and/or  P(2) in the second roll.

         To write here P(2 | 4)  is somehow awkward, if you don't want to deceive yourself and people around, 
         because the outcomes of the first roll and the second roll are independent
         and this independence is obvious and is well known to all, to anyone and to everybody.



RELATED QUESTIONS

bobby has a game where he uses a six sided die. Each side of the die has one of the... (answered by stanbon)
milu is rolling a 6 sided die. She needs to roll a 6 to be able to begin playing a board... (answered by ikleyn)
milu is rolling a 6 sided die. She needs to roll a 6 to be able to begin playing a board... (answered by ikleyn)
A six-sided die is weighted so it rolls 6 five times as often as any other number. If it... (answered by robertb)
Joe rolls 5 consecutive threes on 5 rolls of a fair die. What is the probability that Joe (answered by stanbon)
a fair six-sided die is rolled three times. what is the probability that the sum of the... (answered by EdwinParker)
If you have a fair 6 sided die and you roll it three times, what is the probability that... (answered by Edwin McCravy)
What is the probability that in two rolls of a single die, a man will roll a 2 on the... (answered by ewatrrr)
You roll a fair die three times. What is the probability that a) you roll all 6's?... (answered by ewatrrr)