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# So let's do a vertical comparison here Apollo. I put these

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So let's do a vertical comparison here Apollo. I put these [#permalink]  31 Aug 2006, 07:13
So let's do a vertical comparison here Apollo. I put these on the board in case other members have some shortcuts to add..

Scenario 1:

Set S consists of all non-negative even integers and all integers ending with 3 or 7. If an integer between 1 and 105, inclusive, is selected at random, approx, what is the closest approximation in % to the probability that this integer is a member of set S?

Scenario 2:

Set S consists of all non-negative even integers or all integers ending with 3 or 7. If an integer between 1 and 105, inclusive, is selected at random, approx, what is the closest approximation in % to the probability that this integer is a member of set S?
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Hi Matt

Both scenarios you presented are of mutually exclusive sets. So for the first scenario the Probability of the intersection would be 0

The second scenario 19/105 + 52/105 since again they will not have an intersection you will not need to subtract the elements they have in common
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apollo168 wrote:
Hi Matt

Both scenarios you presented are of mutually exclusive sets. So for the first scenario the Probability of the intersection would be 0

The second scenario 19/105 + 52/105 since again they will not have an intersection you will not need to subtract the elements they have in common

Close, you forgot to add one (twice).

The first scenario is Mut Ex.

To get all multiples of 2 (inclusive) ---> 105-1/2 = 52
To get all numbers ending with 3 (inclusive) ---> 103-3/10+1 = 11
To get all numbers ending with 7 (inclusive) ---> 97-7/10+1 = 10

Mut Ex. Formula: Prob(even)+Prob(3)+Prob(7)/total possibilities

52+11+10/105

Simplify to 73/105 ~70%

Now how could we rewrite this problem so that it wouldn't be Mut Ex?
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GMATT73 wrote:

Now how could we rewrite this problem so that it wouldn't be Mut Ex?

Mutually exclusive events are events that can not be true at the same time. Like flipping of a coin can not result in head and tail at the same time. Its not possible to get a number that have odd unit digit and is even.

Set S = {All multiple of 5}
Set T = {All even numbers}

Set S and T are NOT mutually exclusive. A number could be even and multiple of 5 at the same time.
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IMO the question 1 has no solution. Set S consists of ALL non negative even integers, which are infinite.
From definition of Prob beneficial outcomes, integers that are even or end with 3 or 7 in the interval 1-105, should be related to total outcomes or set S. Since set S is infinite the prob can not be calculated. If we assume that denominator is INF then the prob tends to 0[/i]
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