problem solving
Conditional Probability
One dice is rolled two separate times. Find the probability that the dice lands on an even number both times, and the sum of the two rolls is greater than 6 but the first roll must be larger than the second.
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Solution:
The complete set would consist of the following:
S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
We will let A="even number both times" and B="the sum of the two rolls is greater than 6 but the first roll must be larger than the second"
Therefore: A={(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)} and B={(4,3),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)}
There are 36 total outcomes, so P(AnB)={(6,2),(6,4)}=2/36 and P(B)=9/36
P(A|B)=(2/36)/(9/36)= 2/9
Back to first bonus point opportunity, ECE302 Spring 2013
