div10 wrote:

Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?

M does it in 6 weeks and E does it in 8 weeks, so both combined have to do it in less than 6 weeks...

Both will make it in

1/6+1/8=14/48..

So 48/14 days or two houses in 2*48/14 which is <7

So only when E and M work together it can be less than 7 weeks..

Now what is the probability of that ...

A dice has 6 sides and on roll of two sides, E will work alone

So 2/6=1/3

So >7 weeks is 1-1/3=2/3

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