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?
A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1
B is the OA.
I am confused here. I don't know how to start. With the probability or the rates. Experts, can you show me how to solve this PS question. I'd really like to see the answer.
Mike and Emily need to build 2 identical houses. Mike . . .
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Executive decision: I'm changing the names here.Vincen wrote:Amy and Emily need to build 2 identical houses. Amy, 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, Amy 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?
A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1
B is the OA.
I am confused here. I don't know how to start. With the probability or the rates. Experts, can you show me how to solve this PS question. I'd really like to see the answer.
First, rephrase the question.
If Amy can do 1 house in 6 weeks, she can do 2 in 12 weeks. If Emily can do 1 house in 8 weeks, she can do 2 in 16 weeks. Neither alone can do 2 houses in 7 weeks.
Together: Amy's rate is 1/6 and Emily's rate is 1/8. Their combined rate is 1/6 + 1/8 = 14/48 = 7/24.
Rate and Time have a reciprocal relationship, so the time to do one house together would be 24/7. Thus, the time to do two houses together would be 48/7. This is less than 7.
So our rephrased question: what is the probability that Amy and Emily work together?
Desired outcomes (work together): Roll a 5 or 6 --> so 2 desired outcomes
Total possible outcomes: 6
Desired/Total = 2/6 = 1/3. The answer is B