Probability of Reaction

Probability theory and statistics

Probability of Reaction

Postby Guest » Mon Feb 18, 2019 10:20 am

A person carries 3 bottles of compound X, 3 bottles of compound Y and 3 bottles of compound Z. While X and Y will react vigorously, Z will prevent the reaction from happening. If the person falls and 3 random bottles react, what is the probability that a vigorous reaction will happen?

I tried solving this question like this:
Possible combinations:
ABB
ABA

3/6 x 3/5 x 2/4 = 18/120
3/6 x 3/5 x 2/4 = 18/120

18/120 x 2 = 3/10

I'm wondering if the order of the bottles matter and if the the number of bottles of Z should be counted (e.g. 3/9 x 3/8 x 2/7)?

Please tell me if I'm wrong and provide the right way to do this...
Guest
 

Re: Probability of Reaction

Postby HallsofIvy » Tue Mar 12, 2019 8:55 am

Why are you writing "A"s and "B"s when you are interested in "X"s and "Y"s? In order to have a reaction you must have at least one X and one Y but no Z. The possibilities are
XXY
XYX
YXY
XYY
YXY
YYX
(The way 3 letters can be "X" or "Y" is [tex]2^3= 8[/tex] but we are rejecting "XXX" and "YYY" so there are 8- 2= 6.)

A total of 6 situations out of a total possible of [tex]3^3= 27[/tex] total. The probability is 6/27= 2/9.

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Re: Probability of Reaction

Postby Guest » Sun Mar 24, 2019 10:37 pm

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