Question 1022288
 
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.