P(A|B) = 1/3
What is Venn diagram?
"A Venn diagram in mathematics is a diagram that uses overlapping circles or other shapes to represent the logical relationships between two or more sets of items. "
What is probability?
"For any experiment, a probability denotes the possibility of outcome for any event."
The formula to calculate the probability of an event:
For event A, the probability of event A is,
P(A) = number of favorable outcomes/ total umber of outcomes
What is conditional probability?
"Conditional probability is the probability of an event occurring given that another event has already occurred."
The formula to calculate the conditional probability:
P(A|B) = P(A∩B)÷P(B)
For given diagram:
Let A represents a set of students playing Basketball and B represents a set of students playing Soccer
So, A = {Fran, Ian, Juan, Ella}
⇒ n(A) = 4
B = {Mickey, Marcus, Ella}
⇒ n(B) = 3
(A ∩ B) = {Ella}
⇒ n(A ∩ B) = 1
sample space: S = {Fran, Ian, Juan, Ella, Mickey, Marcus, Mai, Karl, Jada, Gabby}
⇒ n(S) = 10
Now, we calculate probability of B and A∩B.
P(B) = n(B)/n(S)
⇒ P(B) = 3/10
Also, P(A∩B) = n(A∩B) / n(S)
⇒ P(A∩B) = 1/10
So, the required probability would be,
⇒ P(A|B) = P(A∩B) ÷ P(B)
⇒ P(A|B) = (1/10) ÷ (3/10)
⇒ P(A|B) = 1/3
Therefore, P(A|B) = 1/3
Learn more about probability here:
https://brainly.com/question/12478394
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