How do you add probabilities?

pramrok62 2022-09-28 Answered
How do you add probabilities?
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Answers (1)

oldgaffer1b
Answered 2022-09-29 Author has 9 answers
We can add two probabilities as long as the events are disjoint.

Explanation:
Suppose A and B are two events.
P ( A or B occurs ) = P ( A B ) = P ( A ) + P ( B ) + P ( A B )
Here P ( A B ) is the probability that the two events occur simultaneously. If these events are disjoint, P ( A B ) = 0 and in that case we can add the probabilities.
For example: Suppose events A and B are disjoint, P ( A ) = 0.1 , P ( B ) = 0.2 , then P ( A B ) = 0.1 + 0.2 = 0.3
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What is the difference between events that are mutually exclusive and those that are not mutually exclusive?
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The answer should be 1 2450 which presumably comes from 1 50 × 1 49 . But it seems that the order does not count. I did not assume that Alfonso got ticket 14 first then Colin got ticket 23 second.

Update: What is wrong with this reasoning. When I said that I did not assume order, I meant that it's possible

1. Alfonso got ticket 14 first, then Colin got ticket 23,
2. Colin got ticket 23 first, then Alfonso got ticket 14.

Both of these possibilities are possible before the tickets are given out, so we can make an 'or' statement. Label the event Alfonso got ticket 14 by A 14 and Colin got ticket 23 by A 23 . Then by the addition rule
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I realize that once the tickets are sold, then only one of { A 14 C 23   ,   C 23 A 14 } must occur, but before the tickets are sold both possibilities are plausible. Why would the probability change before and after the tickets are sold.
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What is another name for mutually exclusive events?
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I tried to visualize but not able to do so correctly.
11,12,13,14,15,16, 21,22,23,24,25,26,31,32, ....6,6
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A game is played by rolling a six sided die which has four red faces and two blue faces. One turn consists of throwing the die repeatedly until a blue face is on top or the die has been thrown 4 times
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