To find the probability that a randomly selected student attended the game, given that the student is from North Beach, we need to use the concept of conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred.
The conditional probability [tex]\( P(A|B) \)[/tex] is defined as:
[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]
In this problem:
- Event A is the event that a student attended the game.
- Event B is the event that a student is from North Beach.
We are looking for [tex]\( P(\text{Attended the game} | \text{From North Beach}) \)[/tex].
From the table:
- The total number of students from North Beach (Event B) is 200.
- The number of students from North Beach who attended the game (Event A and B) is 90.
Using these numbers, we can find the conditional probability:
[tex]\[ P(\text{Attended the game} | \text{From North Beach}) = \frac{\text{Number of students from North Beach who attended the game}}{\text{Total number of students from North Beach}} \][/tex]
Plugging in the numbers:
[tex]\[ P(\text{Attended the game} | \text{From North Beach}) = \frac{90}{200} \][/tex]
Now, we simplify this fraction:
[tex]\[ \frac{90}{200} = 0.45 \][/tex]
So, the probability that a randomly selected student attended the game, given that the student is from North Beach, is 0.45, which corresponds to option D.
Thus, the correct answer is:
D. 0.45
