SOLUTION: Suppose a die is rolled twice and comes up 4 on the first roll. What is the probability that the second roll is also a 4? (Should I use conditional probability or product rule of p

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Question 1022288: Suppose a die is rolled twice and comes up 4 on the first roll. What is the probability that the second roll is also a 4? (Should I use conditional probability or product rule of probability? Anyway, thanks in advance!)
Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!

Question:
Suppose a die is rolled twice and comes up 4 on the first roll. What is the probability that the second roll is also a 4? (Should I use conditional probability or product rule of probability? Anyway, thanks in advance!)

Solution:
You could use either method, but the results should come up the same.

We assume a fair die.
1. probability product rule:
Probability that the first one is a four = 1 (already happened)
probability that the second one is a four = 1/6.
Product rule: 1*1/6=1/6.

2. conditional probability:
Probability that the first throw is a four = P(4)=1/6
Probability that the second throw is a four = P(4)=1/6
Probability that both are fours: P(4∩4)=(1/6)*(1/6) [product rule]
Probability that the second throw is a four given the first throw is a four
=P(4|4)=P(4∩4)/P(4)=(1/6)*(1/6)/(1/6)=1/6 as before.