Question 1200872: 1. A store has 6 TV Graphic magazines and 8 Newstime magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased. Express your in fraction.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Answer: 48/91
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Explanation:
There are 6 TV Graphic magazines out of 6+8 = 14 magazines total.
6/14 = 3/7 is the probability of selecting a TV Graphic magazine.
While it's not clearly stated in the instructions, I'll assume that the magazines aren't replaced.
Meaning that if a customer purchases a TV Graphic magazine, then the owner won't restock the shelf with that type of magazine. Same goes for Newstime.
If that assumption is true, then the total goes from 14 to 14-1 = 13 after the first magazine is chosen.
8/13 is the probability of selecting a Newstime magazine as the 2nd selection.
(3/7)*(8/13) = (3*8)/(7*13) = 24/91 is the probability of selecting a TV Graphic magazine followed by a Newstime magazine, where no replacement happens.
Through similar calculations
(8/14)*(6/13) = (8*6)/(14*13)
= (2*4*6)/(2*7*13)
= (4*6)/(7*13)
= 24/91
represents the probability of selecting a Newstime magazine first then TV Graphic next (no replacement).
So,
24/91 + 24/91 = (24+24)/91 = 48/91 is the probability of selecting one of each magazine.
In decimal form,
48/91 = 0.52747
when rounding to five decimal places.
There's roughly a 52.747% chance of selecting one of each magazine.
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Another approach:
Imagine a table with the number of TV Graphic magazines as the rows, and the number of Newstime magazines as the columns.
Therefore we have a table with 6 rows and 8 columns.
You don't have to draw out the table. It could be left as a mental thought exercise.
Inside the table are 6*8 = 48 inner cells to represent the 48 different ways to pick one of each magazine brand.
Let's now determine how many ways there are two select any two magazines.
For this paragraph, we won't worry if the two magazines are different.
There are n = 6+8 = 14 magazines total.
We wish to make r = 2 selections where order doesn't matter.
Use the nCr combination formula.
nCr = (n!)/(r!(n-r)!)
14C2 = (14!)/(2!*(14-2)!)
14C2 = (14!)/(2!*12!)
14C2 = (14*13*12!)/(2!*12!)
14C2 = (14*13)/(2!)
14C2 = (14*13)/(2*1)
14C2 = (182)/(2)
14C2 = 91
If you wanted, you can alternatively use Pascal's Triangle to determine this nCr value.
We found that:- There are 48 ways to select one of each magazine.
- There are 91 ways to select 2 magazines (where we may or may not get one of each type).
The order doesn't matter with the magazine selection.
Therefore, we arrive at 48/91 as the probability of selecting one of each magazine.
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