SOLUTION: If one of the 50 states is selected at random to be the site of a new nuclear power plant, find the probability that: a. the state begins with the letter A or the word North. b.

Question 1137248: If one of the 50 states is selected at random to be the site of a new nuclear power plant, find the probability that:
a. the state begins with the letter A or the word North.
b. the state borders Arkansas and begins with the letter T.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Here are two terms we'll use
Sample space = set of all possible outcomes
Event space = set of all outcomes we want to happen

For both parts A and B, the sample space is the same set: the set of all 50 states
You can list out every member of this set, but I don't advise it because how large the set is. Simply giving it a brief description is enough.

For reference, here is the list of 50 states
https://en.wikipedia.org/wiki/List_of_states_and_territories_of_the_United_States

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Part A

In this part, we only care about the states that start with the letter A or have "north" in the name. Those states are
{Alabama, Alaska, Arizona, Arkansas, North Carolina, North Dakota}
which defines the event space.
There are 6 items in the event space out of 50 items in the sample space, so the probability would be 6/50 = 3/25 = 0.12

The answer as a fraction is 3/25
In decimal form that equivalent answer is 0.12
The percentage form is 12%
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Part B

Consult this map (found on the same link as posted earlier above). Note that the following states start with the letter T and they border Arkansas: {Texas, Tennessee}

So there are 2 items in the event space this time. The sample space is still 50 items. Therefore 2/50 = 1/25 = 0.04 is the probability

The probability as a fraction is 1/25
In decimal form that equivalent answer is 0.04
The percentage form is 4%

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