Question 1025243: The probability that Lisa passes her math class is 0.65, the probability that she passes her english class is 0.75, and the probability that she will pass her math class given that she passes her english class is 0.8. Find the probability that she will pass
1. Both her classes
2. Neither of her classes
I don't know if I am setting up the problem correctly, for the first problem do I have to apply the multiplication rule?
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Question:
The probability that Lisa passes her math class is 0.65, the probability that she passes her English class is 0.75, and the probability that she will pass her math class given that she passes her English class is 0.8. Find the probability that she will pass
1. Both her classes
2. Neither of her classes
I don't know if I am setting up the problem correctly, for the first problem do I have to apply the multiplication rule?
Solution:
Let
E = event of passing English, and
M = event of passing math.
which means P(E)=0.75, and P(M)=0.65 from given information.
Yes, you apply the multiplication rule for part 1, using P(M)=0.65, and P(E)=0.75.
For part two, you need to find P(~M∩~E), which equals 1-P(M∪E), since the two events are assumed to be independent.
Either way, you will need the given conditional probability of 0.8, which is defined as P(M|E)=P(M∩E)/P(E) to solve for P(M∩E).
Then you'll substitute P(M∩E) into the relationship P(M∪E)=P(M)+P(E)-P(M∩E) to find the probability of passing neither ( P(~M∩~E), which equals 1-P(M∪E) )
It is encouraging that you show your efforts in solving the problem. Please continue to do so, and I am sure you will continue to improve your probability skills.
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