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Ugly Multiplication

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by damilolaamele » Sun Mar 03, 2013 10:28 pm
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?

[spoiler]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%[/spoiler]

Please can someone explain how (9/10)^10 was broken down to 0.348 without using a calculator or having to do a messy multiplication?

Thanks!

Source: GMAT Math Tough Problems. I got document somewhere on the BTG website but I can't remember where exactly.
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by Anurag@Gurome » Sun Mar 03, 2013 10:43 pm
damilolaamele wrote:Please can someone explain how (9/10)^10 was broken down to 0.348 without using a calculator or having to do a messy multiplication?
I can't think of any easy way to do this except approximating the multiplications in each step as follows,

9/10 = 0.9

2 --> (0.9)*(0.9) = 0.81
3 --> (0.81)*(0.9) ≈ 0.73
4 --> (0.73)*(0.9) ≈ 0.65
5 --> (0.65)*(0.9) ≈ 0.59
6 --> (0.59)*(0.9) ≈ 0.53
7 --> (0.53)*(0.9) ≈ 0.48
8 --> (0.48)*(0.9) ≈ 0.43
9 --> 0.43)*(0.9) ≈ 0.39
10 --> (0.39)*(0.9) ≈ 0.35
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by damilolaamele » Sun Mar 03, 2013 11:03 pm
Wow! Still looks pretty tough to me but it sure is a better approach than raw multiplication. Thank you very much
Anurag@Gurome wrote:
damilolaamele wrote:Please can someone explain how (9/10)^10 was broken down to 0.348 without using a calculator or having to do a messy multiplication?
I can't think of any easy way to do this except approximating the multiplications in each step as follows,

9/10 = 0.9

2 --> (0.9)*(0.9) = 0.81
3 --> (0.81)*(0.9) ≈ 0.73
4 --> (0.73)*(0.9) ≈ 0.65
5 --> (0.65)*(0.9) ≈ 0.59
6 --> (0.59)*(0.9) ≈ 0.53
7 --> (0.53)*(0.9) ≈ 0.48
8 --> (0.48)*(0.9) ≈ 0.43
9 --> 0.43)*(0.9) ≈ 0.39
10 --> (0.39)*(0.9) ≈ 0.35
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by Brent@GMATPrepNow » Mon Mar 04, 2013 8:48 am
I'd be very surprised if an official GMAT question asked you to evaluate (9/10)^10.
GMAT math questions are designed to test your number sense and your logic skills. They are not designed to test your ability to carry out lengthy calculations

If you were (somehow) asked to actually evaluate (9/10)^10, the answer choices would be such that you could identify the correct answer without performing all of those calculations.

Cheers,
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