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Answer:
The probability that a fan is waving a banner given that the fan is cheering for team A is 0.25.
Step-by-step explanation:
The percentage of fans cheering for team A is, 80%.
The percentage of fans waving banners and cheering from team A is, 20%.
The probability that a fan is cheering is: P (C) = 0.80.
The probability that a fan is waving banners and cheering is:
P (W ∩ C) = 0.20.
The conditional probability of an event X provided that another event A has already occurred is:
[tex]P(X|A)=\frac{P(X\cap A)}{P(A)}[/tex]
Compute the conditional probability that a fan is waving a banner given that the fan is cheering for team A as follows:
[tex]P(W|C)=\frac{P(W\cap C)}{P(C)}=\frac{0.20}{0.80}= 0.25[/tex]
Thus, the probability that a fan is waving a banner given that the fan is cheering for team A is 0.25.
The probability that a fan is waving a banner given that the fan is cheering for team A is 0.25.
The percentage of fans cheering for team A is, 80%.
P (A) = 0.80.
The percentage of fans waving banners and cheering from team A is, P(B ∩ C)=20%.=0.20
The probability that a fan is waving banners and cheering is
P (W ∩ A) = 0.20.
We have to calculate the probability that a fan waved a banner give that the fan cheered for team A
What is the formula the conditional probability of an event X provided that another event A has already occurred ?
The conditional probability of an event X provided that another event A has already occurred is:
[tex]P(x|A)=\frac{P(X \cap A )}{P(A)}[/tex]
Therefore use the given value in above formula we get,
Compute the conditional probability that a fan is waving a banner given that the fan is cheering for team A as follows:
[tex]P(W|A)=\frac{W\cap(A) }{P(A)}=\frac{0.20}{0.80} =0.25[/tex]
Therefore,the probability that a fan is waving a banner given that the fan is cheering for team A is 0.25.
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