Difference between revisions of "ECE 302-Extra Credit- Zimmerman" - Rhea

Revision as of 16:39, 26 January 2013

problem solving 

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.

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

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