babulsaha wrote:
Question:
1) Find the number of children a couple should have in order that the probability of their having at least 2 boys will be greater than 0.75.
2) Assuming that each dart has probability 0.20 of hitting its target, find the number of darts one should throw at a target in order that the probability of at least 2 hits will be greater than 0.60.
Could you please anybody reply on the above.
Dear
babulsahaMy friend, first of all, when you have math questions, please post them in the math forum. This "ask GMAT expert" forum is for general test advice, strategies, study advice, etc., not for specific math and verbal questions. Does this make sense?
Second, both of these questions are WAY TOO HARD to be relevant to the GMAT. They are way beyond what the GMAT tests, even on its hardest Quant questions.
Having said that, I like math, so I am happy to answer.
The first one is surreal in a way. I assume the question means --- what's the number of children, when the couple is starting from scratch with no children? Of course, with the birth of each child, the probability would change. I assume you mean an "all at once" kind of calculation. For that, this is an exceedingly poor scenario. I will suggest the alternate question which I think gets to the hear of what #1 is trying to ask:
1a)
Find the minimum number of fair coins someone should toss simultaneously so the probability of getting at least 2 heads is greater than 0.75.
Frankly, the only quick way I know how to solve this is with a calculator. This is yet another reason why it is entirely inappropriate as a GMAT Quant question.
Technically, the equation would be
P = 1 - n(0.5)^(n) - (0.5)^n > 0.75
Again, I know of absolutely no easy way to do this without a calculator.
With 6 coins, the probability of at least two heads is 0.65625
With 7 coins, the probability is 0.7734375
Thus, N = 7 is the lowest value for which this is true.
2)
Assuming that each dart has probability 0.20 of hitting its target, find the number of darts one should throw at a target in order that the probability of at least 2 hits will be greater than 0.60.
Again, the probability would change with each dart, so I am assuming, essentially, one fires N darts simultaneously, and they are all independent, and each has a probability of 0.4.
The set up
P = 1 - n(0.4)(0.6)^(n-1) - (0.6)^n
Again, essentially impossible without a calculator.
For n = 8, P = 0.68460544
For n = 9, P = 0.768212992
These are questions typical, say, of AP Statistics or some challenging course on probability. These are most certainly NOT GMAT-like questions.
Does all this make sense?
Mike