For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
07/11/2012

PROBLEM # 1
Player A has one more coin than player B. Both players throw all of their coins simultaneously and observe the number that come up heads. Assuming all the coins are fair, what is the probability that A obtains more heads than B?

PROBLEM # 2

Two students play a game based on the total roll of two standard dice. Student A says that a 12 will be rolled first. Student B says that two consecutive 7s will be rolled first. The students keep rolling until one of them wins. What is the probability that A will win?

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Problems from 07/05/12

PROBLEM #1
What triangle with the given perimeter would have the largest area.?

SOLUTION 1
Equilateral.

PROBLEM #2
Calculate integral of arctan(x) dx from -1 to 1.

SOLUTION 2
pi/3.

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