Question 1201433: Mr. C. Nile and Mr. D. Mented agreed to meet at 8 P.M. in one of the Spanish restaurants in Ybor City. They were both punctual, and they both remembered the date agreed on. Unfortunately, they forgot to specify the name of the restaurant. If there are 3 Spanish restaurants in Ybor City, and the 2 men each go to 1 of these, find the probability that the following occurs. (Enter your probabilities as fractions.)
a) They meet each other.
b) They miss each other.
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Thank you!
Found 3 solutions by ikleyn, math_tutor2020, greenestamps:
Answer by ikleyn(52794)   (Show Source):
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Answers:
a) 1/3
b) 2/3
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Explanation:
I'll refer to the persons as C and D.
I'll also refer as the restaurants as R1,R2,R3.
Let's say C picks R1.
D has probability 1/3 of also picking R1.
This logic applies if C chose R2, or R3.
Effectively we can make person C the anchor, and have the question be reframed to "What are the chances person D picked the anchor restaurant?". The order of the restaurants doesn't matter, and neither does the order of who selects first.
Therefore, the chances of them meeting is 1/3
The chances of them missing each other is 1 - (1/3) = 2/3
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Another approach:
Form a table showing all possible combos
C's choices are along the top
D's choices are along the left side
The X's refer to instances where they meet. Otherwise, they miss each other.
There are 3*3 = 9 outcomes total
There are 3 X's out of 9 slots total.
3/9 = 1/3 = chances of them meeting
6/9 = 2/3 = chances of them missing each other.
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Edit:
Another approach:
Using inspiration from the tutor @ikleyn, we can have the following
X = P(C picks R1, D picks R1) = P(C picks R1)*P(D picks R1) = (1/3)*(1/3) = 1/9
Y = P(C picks R2, D picks R2) = P(C picks R2)*P(D picks R2) = (1/3)*(1/3) = 1/9
Z = P(C picks R3, D picks R3) = P(C picks R3)*P(D picks R3) = (1/3)*(1/3) = 1/9
Then X+Y+Z = (1/9)+(1/9)+(1/9) = 3/9 = 1/3 represents the chances of them meeting, and 2/3 is the chance of them not meeting.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
One basic method for computing probabilities like this is to find the probability that you can still get the desired outcome when the first person chooses a restaurant, then find the probability that you can still get the desired outcome when the second person chooses a restaurant, then multiply the two probabilities.
The first person can choose any of the 3 restaurants; the probability that we can still get the desired outcome after the first person chooses a restaurant is 3/3 = 1.
Then to get the desired outcome, the second person has to choose the same restaurant as the first person; there are 3 restaurants to choose from, and only 1 will give the desired outcome. So the probability that the second person makes a choice that will result in the desired outcome is 1/3.
And the probability of obtaining the desired outcome is then the product of the two probabilities: (1)*(1/3) = 1/3.
ANSWER: 1/3
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