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'''Conditional Probability''' | '''Conditional Probability''' | ||
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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.<br> | 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.<br> | ||
Latest revision as of 18:18, 27 January 2013
problem solving
Conditional Probability
Problem:
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
