The probability that a person likes football, given that she does not like basketball, is 63.3%, as calculated using the conditional probability formula with values from the provided table.
The table shows the number of people who like to watch football and basketball in a sample of 100 people.
The probability that a person likes to watch football, given that she also likes to watch basketball, is calculated by dividing the number of people who like both sports by the number of people who like basketball. This is called the conditional probability formula:
P(F|B) = P(F ∩ B) / P(B)
Using the table, we can find the values of P(F ∩ B) and P(B):
P(F ∩ B) = 27/100 = 0.27
P(B) = (27 + 13)/100 = 0.4
Plugging these values into the formula, we get:
P(F|B) = 0.27 / 0.4 = 0.675
This means that the probability that a person likes to watch football, given that she also likes to watch basketball, is 67.5%. This is a different conditional probability, and we need to use a different formula:
P(F|¬B) = P(F ∩ ¬B) / P(¬B)
Here, ¬B means the complement of B, or the event that a person does not like to watch basketball. We can find the values of P(F ∩ ¬B) and P(¬B) from the table:
P(F ∩ ¬B) = 38/100 = 0.38
P(¬B) = (38 + 22)/100 = 0.6
Plugging these values into the formula, we get:
P(F|¬B) = 0.38 / 0.6 = 0.633
This means that the probability that a person likes to watch football, given that she does not like to watch basketball, is 63.3%.
Therefore, the answer to your question is 63.3%.
Complete question:
Sports again From Exercise 3, if someone doesn’t like to watch basketball, what is the probability that she will be a football fan?