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Description:

Statistics, Data, and Probability I: Drill Set 5, Problem 5. What is the probability that, on the second draw, a vowel will be chosen?

Language:
English Language

Transcript

00:03

Here's a shmoopy question for you...

00:06

There is a crisis at Sesame Street.

00:08

The residents there are in urgent need of 2 letters.

00:11

According to the laws of the land, those letters must be chosen at random from an alphabet

00:16

set consisting of both upper- and lowercase letters.

00:20

If, on the first random draw, the letter capital 'E' was chosen and eliminated from the Cookie

00:26

Monster's garbage can of available letters... ...what is the probability that, on the second

00:32

draw, a vowel will be chosen?

00:34

Assume the letters 'y' and 'Y' are consonants...

00:38

And here are the potential answers:

00:43

Life may look easy on the Street but it isn't always.

00:46

The puppets there wrestle with big ideas. And sometimes with each other.

00:51

So what is this question really asking? It's a probability question with a twist on the

00:55

total set of possible choices.

00:57

The basic alphabet has 26 letters -- but the twist is that this problem treats capital

01:03

letters different from small letters...

01:05

...kinda like fancy computer password log ins these days.

01:08

So there are 52 total choices of letters in the mega set of possibilities.

01:13

To now get to the answer, we have to assess the "damage" given by the other twists

01:17

the problem throws at us.

01:18

First of all, the capital E is removed -- it's a vowel and it's also one of the 52 choices.

01:25

So now we know the denominator has to have 51 in it, not 52.

01:30

We know that there are 5 vowels in the alphabet -- but there are 10 choices if we can count

01:35

both a capital and a small letter. And we have removed a capital E from the possible

01:40

picks moving forward.

01:41

So there are just 9 vowels left as possible

01:44

picks over the total set of 51... ... so our answer is 9 over 51. Choice C.

01:51

Or should that be... choice... lowercase c? Uh oh, we're feeling overwhelmed...

01:55

Where's Elmo when you need him?

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