Math Destroyer Practice Test 1 #23

[madirocks]

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It is know that 20% of the population of Smallville has blue eyes. If four people are chosen at random from this population, what is the probability that at least one of the four has blue eyes?

A. (1/5)^4 = 1/625
B. (4/5)^4 = 256/625
C. 1 - (1/5)^4 = 624/625
D. 1 - (4/5)^4 = 369/625
E. (4/5)^1 + (1/5)^3 = 101/125
(the answer is D)
A detailed explanation would be appreciate...thanks =)

 

[lyjw88]

since 1/5 of the population has blue eyes, 4/5 does not.
so you calculate the probability of choosing four people WITHOUT blue eyes and substract that value from 1.

 

[kgupta3]

I don't understand why this answer is found by starting with the percentage of students who DON'T have blue eyes. Why not just start with the percentage of students who do have them.

How is answer choice D different from A. I see the steps on how to solve the problem but I don't get the logic behind it.

 

[KyoPhan]

I, too similarly thought about working with those who had blue eyes. The problem is that you run into this trouble. First you have to figure out the probability of picking out only 1 with blue eyes. THen you have to figure out the probability of picking out 2 blue eyes. Then 3, and then 4. Once you figure out all that, you would add them up to get the answer.

It is much easier to just figure out the following question:
What is the probability of picking out ALL non-blue eyes? That is (1/5)^4.

All other choices will have some sort of blue eyes in it. So to get the answer, we take 1-(4/5)^4.

 

[LetsGo2DSchool]

The important and most valuable thing about this particular problem as well as others in Math Destroyer is not whether or not the solution makes logical sense to you. The beauty is that if you encounter any similar problems on the DAT, then you'll know exactly how to solve it, not to mention accomplishing it very quickly. Imagine others who would sit there wasting a good 3-4 minutes going in brain circles and ending up with an answer that's not even one of the answer choices.

 

[kgupta3]

thanks guys, it all makes sense now!

 

[NewBee12]

To do this problem the long way you have to find the probability of exactly 1 having blue eyes then 2 having blue eyes then 3 then 4 and then add them all up. That's way too long. The shorter way is to find the probability of none having blue eyes raise it to the fourth power andsubstract from 1.
I hope this helps

 

[Dentist335]

Im sorry but im still working on brishing some basic cobwebbs off my math skills. why do we subtract from 1 and in which case would we subtract from anything greater than 1 if possible? Im also assuming we raised it to the ^4 because there are a total of 4 ppl choosen from the population? Thanks everyone 🙂

 

[Daneosaurus]

Im sorry but im still working on brishing some basic cobwebbs off my math skills. why do we subtract from 1 and in which case would we subtract from anything greater than 1 if possible? Im also assuming we raised it to the ^4 because there are a total of 4 ppl choosen from the population? Thanks everyone 🙂

Probability is a decimal between 1 and 0, inclusive. 1=100%, or in this case, total number of people in the population. You subtract from 1 because it is quicker than adding.

 

[clutchfans]

At least one is the opposite of zero. probablity of zero blue eyes + probablity of at least 1 blue equals 1 (100%)
P(x>=1) + P(0) = 1
P(0) = (4/5)^4 = 256/625
P(x>=1) = 1- P(0) = 1- 256/625 = 369/625