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by tmontgomery » Fri Sep 04, 2015 1:37 pm
In a certain city in September, there is a 50% chance the high temperature on any day will be greater than 70 degrees. In a 5-day period, what is the probability that the high temperature will be (not necessary in the the order of) 69,75,70,72, and 75?
A. 5/13
B. 7/20
C. 2/5
D. 1/4
E. 5/16
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by Matt@VeritasPrep » Fri Sep 04, 2015 4:54 pm
This seems like a flawed question - we know the probability of the temperature being over 70, but we don't know the probabilities of any specific temperatures, so we can't answer.

I think I know what the author is going for, though: we're essentially being asked for the probability of having the temperature be ≤70, >70, ≤70, >70, and >70 in some order.

Each of those outcomes has a probability of (1/2) on its own, so we start with (1/2)*(1/2)*(1/2)*(1/2)*(1/2). We then have to think of all the orders in which these events could happen.

Since we have three days Over 70 and two days Not Over 70, we're looking for the number of ways to arrange the letters O O O N N. This is 5!/(3!*2!), or 10.

So there are TEN arrangements, each of which has a probability of (1/32). Hence our probability is 10*(1/32), or 5/16.
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by tmontgomery » Fri Sep 04, 2015 11:09 pm
Thank you so much! That helps a lot. However, I'm a little confused at how you got 1/32 for the ten arrangements.
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by Max@Math Revolution » Sat Sep 05, 2015 9:48 pm
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


In a certain city in September, there is a 50% chance the high temperature on any day will be greater than 70 degrees. In a 5-day period, what is the probability that the high temperature will be (not necessary in the the order of) 69,75,70,72, and 75?
A. 5/13
B. 7/20
C. 2/5
D. 1/4
E. 5/16

there is 50% chance that the temperature on any day is greater than 70 degrees is, and among 69,75,70,72,75 there are three days that are higher than 70. Thus the number of cases is 5C3=5*4*3?3*2?1=10. Since all of them have 50% chance, and the chance of temperature being 69,75,70,72,75 is (1/2)(1/2)(1/2)(1/2)(1/2)=1/32. Since we have 10 cases of this, for example, 69, 70, 72, 75, 75등.... the answer is 10*(1/32)=5/16. Thus the answer is E.



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