# Help with finding indicated probability

##### New Member
I have worked on this problem now for the whole entire day, and still don't understand what I am doing wrong. Can someone help me?

The problem states:

9) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results.

Waiting Time (minutes) Number of Customers
0-3 9
4-7 13
8-11 11
12-15 6
16-19 6
20-23 1
24-27 1

a) If we randomly select one of the times represented in the table, what is the probability that it is at least 12 minutes or between 8 and 15 minutes?

The steps I have taken so far is to add all the numbers up to get the total number of customers (47 total)

Then I try to see what the probability is of at least twelve minutes or between 8 and 15 minutes. I added 11 + 6 to get 17, divided that by 47, and got the answer .362. Somehow, I do not think that I am grasping the entire concept. Can someone point me in the right direction? I would greatly appreciate it.

#### vinux

##### Dark Knight
a) If we randomly select one of the times represented in the table, what is the probability that it is at least 12 minutes or between 8 and 15 minutes?
I didn't get what you meant by above statement. Is it you are randomly taking from the table or randomly taking an obs from 47 observation( this make sense).

is it probability is of at least twelve minutes ? or
probability is between 8 and 15 minutes or
combined(with OR)?

##### New Member
You are choosing one time randomly from the table, what is the probability that the time is at least 12 minutes or between 8 and 15 minutes.

#### Dragan

##### Super Moderator
You are choosing one time randomly from the table, what is the probability that the time is at least 12 minutes or between 8 and 15 minutes.

Did you try using: Pr{A Union B} = Pr{A} + Pr{B} - Pr{A Intersects B}?

That is, Pr{A} = Pr{X>=12} = (6+6+1+1)/47; Pr{B} = Pr{8< X <15} = (11 + 6)/47; and Pr{A Intersects B} = 6/47.

And thus,

Pr{A Union B} = 14/47 + 17/47 - 6/47 = 0.532.

Does this point you in the right direction?

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