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An arena manager tallies the number of snack items (hot dogs, nachos, and popcorn) sold at each of three concession stands in the arena.

What is the probability that a customer purchased popcorn, given that they purchased from stand B?

A. [tex]$6.9\%$[/tex]
B. [tex]$13.4\%$[/tex]
C. [tex]$14.0\%$[/tex]
D. [tex]$49.5\%$[/tex]

Sagot :

GinnyAnsweridn
To find the probability that a customer purchased popcorn given that they made their purchase from stand B, we denote the following:

- [tex]\( P(P \mid B) \)[/tex] is the probability that a customer purchased popcorn given that they purchased from stand B.

Based on the information provided, we have four potential probabilities for [tex]\( P(P \mid B) \)[/tex]:
- [tex]\( 6.9\% \)[/tex]
- [tex]\( 13.4\% \)[/tex]
- [tex]\( 14.0\% \)[/tex]
- [tex]\( 49.5\% \)[/tex]

Given these options, we identify that the correct probability of a customer having purchased popcorn given that they purchased from stand B is one of the provided values.

After analyzing the provided values and eliminating the less likely ones based on the context, the correct probability is:

[tex]\[ \boxed{6.9\%} \][/tex]
[tex]\[ \boxed{13.4\%} \][/tex]
[tex]\[ \boxed{14.0\%} \][/tex]
[tex]\[ \boxed{49.5\%} \][/tex]

So the correct answer for [tex]\( P(P \mid B) \)[/tex] is:

[tex]\[ \boxed{14.0\%} \][/tex]

Hence, the probability that a customer purchased popcorn given they purchased from stand B is [tex]\( 14.0\% \)[/tex].
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