Yahoo Answers: Answers and Comments for Probability question? [Mathematics]
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From Patrick H
enAU
Fri, 09 Aug 2013 01:31:07 +0000
3
Yahoo Answers: Answers and Comments for Probability question? [Mathematics]
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https://au.answers.yahoo.com/question/index?qid=20130809013107AAtdvgS
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From MathMan TG: P( at least one A ) = 1  P (no A's) =
1 ...
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https://au.answers.yahoo.com/question/index?qid=20130809013107AAtdvgS
Sat, 10 Aug 2013 00:54:05 +0000
P( at least one A ) = 1  P (no A's) =
1  (26C7) / (30C7) = 0.67688 = 0.68
P( at least 2 B) =
1  P(0 B)  P(1 B) =
1  (22 choose 7)/(30 choose 7)  (8 * 22 choose 6) / 30 choose 7
= 0.70299 = 0.62302
~ ~ ~ Agree with your numbers so far ~ ~ ~
P(A and B) is not simply P(A) * P(B)
because they are not independent.
Intuitively, consider this:
P(B occurs) is based on having 7 chances to draw 2 B's.
Suppose the first card drawn is an A (and therefore event A has occurred).
Now you only have 6 shots at drawing 2 B's, which makes it less likely to occur.
That's over simplified, but it gives you the general idea:
If A occurs, B is somewhat less likely to occur,
and if B occurs, A is somewhat less likely to occur.
P( A and B) = 1  (don't get an A and 2 B's)
This is a rather complex calculation.
If can fail as follows:
A B C
0 * * = 26C7
1+ 0 * = 22C7  18C7 [ all AC only  C only ]
1+ 1 * = 8 * (22C6  18C6) [ 1 B and ( 6 AC  C only ) ]
= 1244912
Total draws = 30 choose 7 = 2035800
P(not ( A & B) ) = 0.6115
P (A and B) = 1  0.6115 = 0.3885
Finally,
P( A or B) = P(A) + P(B)  P(A & B) = .68 + .62  .39 = 0.91
~ ~ ~ end of disagreement section ~ ~ ~
And yes P(A or B) must be higher than either of them individually,
because A or B includes each of the other two as a subset.
Your formula P(A) + P(B)  P(A & B) is correct,
and produces the correct result once you have the right
value for P(A & B).

From DroningOn: it is 0.88 and yes, the probability of either ...
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https://au.answers.yahoo.com/question/index?qid=20130809013107AAtdvgS
Fri, 09 Aug 2013 08:35:00 +0000
it is 0.88 and yes, the probability of either event happening will always be more than both happening at same time

From Anonymous: the answer is 42, that is all
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https://au.answers.yahoo.com/question/index?qid=20130809013107AAtdvgS
Fri, 09 Aug 2013 08:32:09 +0000
the answer is 42, that is all