How do we know in probability question that its AND or OR question.
AND = Multiplication
Please help, i'm messing up simple problems because of this little confusion.
if you're calculating the probability of MULTIPLE events occurring, you always MULTIPLY;
if you're calculating the probability of ALTERNATIVE events occurring, you ADD.
Some common multiple event words: "and", "both" and "all".
Some common alternative event words/phrases: "or", "at least" and "at most".
On the toughest probability questions, you may have to do a bit of both. For example:
At a certain university, the probability of getting on campus housing in any given year is 1/3. If Yohann enters the lottery two years in a row, and if each lottery is independent, what's the probability that Yohann gets housing in exactly one of the two years?
Since there are two years, there are four possible scenarios for Yohann:
1) Yr 1 housing, Yr 2 housing;
2) Yr 1 housing, Yr 2 no housing;
3) Yr 1 no housing, Yr 2 housing; and
4) Yr 1 no housing, Yr 2 no housing.
We want Yohann to get housing in exactly one of the two years, so scenarios (2) and (3) match our desired outcome; in other words, we want scenario (2) OR scenario (3).
So, we begin by calculating the probabilities of scenarios (2) and (3):
For (2), we want a yes AND a no (so we multiply): (1/3)(2/3) = 2/9
For (3), we want a no AND a yes (so we multiply): (2/3)(1/3) = 2/9
However, we're happy with (2) OR (3), so we find the final answer by ADDING those two probabilities:
(2/9) + (2/9) = 4/9
* * *
Hope that helps!
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