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].
