Problem Solving

What is the simplest way to calculate the solution below? It would take forever to calculate (9/10)^10

4. In a basketball contest, players must make 10 free throws. Assuming a player has 90% chance of making each of his shots, how likely is it that he will make all of his first 10 shots?

Ans: The probability of making all of his first 10 shots is given by
(9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10) = (9/10)^10 = 0.348 => 35%

Welcome to the forums, aschaves,

Search some threads I think we already have a discussion related to your query.

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aschaves wrote:What is the simplest way to calculate the solution below? It would take forever to calculate (9/10)^10

4. In a basketball contest, players must make 10 free throws. Assuming a player has 90% chance of making each of his shots, how likely is it that he will make all of his first 10 shots?

Ans: The probability of making all of his first 10 shots is given by
(9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10) = (9/10)^10 = 0.348 => 35%

making it a separate thread, so that members could help you

Does any one know a short cut or has any one found a post related to this?

Its quite easy to get the ans - just time consuming so a shortcut would be great :)

thanks

I think all depends upon the answer choices

here we need to find 9^10/10^10

i.e (9^2) ^ 5 / 10 ^ 10
i.e 81 ^ 5 /10 ^ 10

we can say 81 ~ 80

so it is 80 ^ 5/10 ^ 10

hence we have 8^ 5 /10 ^5

i.e 2^15 /10 ^5

now 2 ^ 10 =1024
so we can easily calculate 2^ 15 as 327... something/100000

so prob is .327.. (i.e.probabilty always lies between 0 & 1)

now our actual probalilty must be something little greater than .327...

so answer choices less than this can be eliminated

so it must be .35 if all other answer choices are greater than .4's

In my opinion in such problems the GMAT requires us to answer the questions with plausible certainity & not complete certainity (better but will consume more time)
so if you can find either the Min or Max extreme of the answer choice, the
other extreme would be taken care by the answer choices.

Thanks again Samir