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Difficult probability and graph theory Question. NOT GMAT

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Difficult probability and graph theory Question. NOT GMAT [#permalink] New post 19 Jun 2013, 06:26
Hi,
My employer is running this quiz which I really want to win. Please can anyone of you give me solutions to few of them. Any help will be appreciated.

3. Suppose X is an arbitrary numeric random variable. Define the variable Y as Y=(X-Minimum(X))/(Maximum(X)-Minimum(X)). Then what is the range of values of Y.
4. Let A and B be two events. Then which one among P(A and B) and P(B) will be larger and why?
5. We have an array of number X(i), I = 1 to n. Give me the algorithm to sort the array X in ascending order.
10. An unbiased coin was tossed 50 times and all the time HEAD appeared. What is the probability of getting HEAD in 51st toss?
11. State with justification whether the following statement is true or false. “Given any group of 5 people there will always be 3 people who know each other or there will be three people who do not know each other.”

P.S. These question have little in common with GMAT. But don't know any other place where chances of getting solution would be more than in here.
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Joined: 24 Jul 2011
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GMAT 1: 780 Q51 V48
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Re: Difficult probability and graph theory Question. NOT GMAT [#permalink] New post 20 Jun 2013, 19:36
3. Y=(X-Minimum(X))/(Maximum(X)-Minimum(X))
What is the highest value that X can take? This is Maximum(X).
What is the lowest value that X can take? This is Minimum(X).
So highest value of the expression = (Maximum(X)-Minimum(X))/(Maximum(X)-Minimum(X)) = 1
Lowest value of the expression = (Minimum(X)-Minimum(X))/(Maximum(X)-Minimum(X)) = 0
Therefore the range of Y is [0,1].

4. P(B) will be larger. The probability of both events occurring is lower than that of only one occurring.

5. Look up 'bubble sort' and how it works

10. The probability of getting Heads remains 1/2 as all the tosses are independent events

11. The statement is false. The minimum number of people required to guarantee this outcome is six.
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Re: Difficult probability and graph theory Question. NOT GMAT   [#permalink] 20 Jun 2013, 19:36
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Difficult probability and graph theory Question. NOT GMAT

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