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SAT Math 1.3 Statistics and Probability 276 Views
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Description:
SAT Math 1.3 Statistics and Probability. Approximately what is the probability that they will be placed in alphabetical order?
Transcript
- 00:02
Here’s your shmoop du jour, brought to you by Bookshelves.
- 00:06
They’re those antiquated things you can… put your Kindle on.
- 00:12
Four books, each with different titles, are going to be placed on a shelf.
- 00:16
Approximately what is the probability that they will be placed in alphabetical order?
- 00:21
And here are the potential answers…
Full Transcript
- 00:27
No matter how many books we have, there is only one way
- 00:30
to put them in alphabetical order if they all have different titles.
- 00:33
So…out of all of the different ways to order these books, only one is a favorable outcome.
- 00:40
Since probability can be calculated with the formula: favorable over number of possible ways…
- 00:47
…we only need to figure out the number of possible ways to solve this problem.
- 00:51
The possible ways we can order 4 books sounds like a permutations problem.
- 00:56
There are 4 slots in which we can place books.
- 00:59
In the first slot, there are 4 choices…meaning if we were to randomly choose a book to put there,
- 01:03
any of the 4 would be fine and dandy. Now, we have 3 left.
- 01:08
In the second slot, there are 3 to choose from, since we already placed the first one.
- 01:13
Next, there are 2 to choose from, and then only 1.
- 01:16
We multiply all of these numbers together to find out the total number of possible permutations.
- 01:22
When we randomly place books, there are 24 ways to place 4 of them.
- 01:26
Out of those 24, only 1 is in alphabetical order.
- 01:31
That comes out to be about to be 1 over 24 or about 4%, so our answer is (B).
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