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SAT Math 1.3 Statistics and Probability
276 Views

SAT Math 1.3 Statistics and Probability. Approximately what is the probability that they will be placed in alphabetical order?

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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?

Language:
English Language

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…

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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