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20 Jul 2023, 08:00
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C
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At a restaurant, three couples are preparing to order dessert. If there are 9 different desserts on the menu, what is the probability that the husband and wife of each couple will order the same dessert? Note that while each couple is required to order the same dessert, this dessert does not need to match the one ordered by the other couples.
A. 6/9^3
B. 3/9^3
C. 1/9^3
D. 1/9^6
E. 6/9^6
A. 6/9^3
B. 3/9^3
C. 1/9^3
D. 1/9^6
E. 6/9^6
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24 Aug 2023, 02:04
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Official Solution:
At a restaurant, three couples are preparing to order dessert. If there are 9 different desserts on the menu, what is the probability that the husband and wife of each couple will order the same dessert? Note that while each couple is required to order the same dessert, this dessert does not need to match the one ordered by the other couples.
A. \(\frac{6}{9^3}\)
B. \(\frac{3}{9^3}\)
C. \(\frac{1}{9^3}\)
D. \(\frac{1}{9^6}\)
E. \(\frac{6}{9^6}\)
For each couple, there's a 1/9 chance the wife will order the same dessert as her husband. With three couples, the combined probability is:
\(\frac{1}{9} *\frac{1}{9} *\frac{1}{9} = \frac{1}{9^3} \).
Answer: C
At a restaurant, three couples are preparing to order dessert. If there are 9 different desserts on the menu, what is the probability that the husband and wife of each couple will order the same dessert? Note that while each couple is required to order the same dessert, this dessert does not need to match the one ordered by the other couples.
A. \(\frac{6}{9^3}\)
B. \(\frac{3}{9^3}\)
C. \(\frac{1}{9^3}\)
D. \(\frac{1}{9^6}\)
E. \(\frac{6}{9^6}\)
For each couple, there's a 1/9 chance the wife will order the same dessert as her husband. With three couples, the combined probability is:
\(\frac{1}{9} *\frac{1}{9} *\frac{1}{9} = \frac{1}{9^3} \).
Answer: C
General Discussion
20 Jul 2023, 08:16
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Bunuel
There are 9 different desserts and the couple (husband and wife) have to choose the same dessert.
So probability of them ordering the same dessert is 1/9
Since there are 3 couples, it will be 1/9 x1/9 x 1/9
Therefore answer is C 1/9^3
