Respuesta :
Answer
Option B is correct.
The probability that a student passes the test given that he or she took the class = P(A | B) = (82/115)
Explanation
The probability that a student passes the test given that he or she took the class is called conditional probability.
In conditional probability, the probability that event A occurs given that event B has already occured is presented as P(A | B) and it is given mathematically as
P(A | B) = P(A n B) ÷ P(B)
For this question, we are asked to find the probability that a student passes the test given that he or she took the class
The probability that a student passes the test
= P(A) = (82 + 23) ÷ (82 + 33 + 23 + 21) = (105) ÷ (159) = (105/159) = (35/53) = 0.6604
The probability that a student took the class
= P(B) = (82 + 33) ÷ (82 + 33 + 23 + 21) = (115) ÷ (159) = (115/159) = 0.7233
The probability that a student passes the test and took the class
= P(A n B) = (82) ÷ (82 + 33 + 23 + 21) = 82 ÷ 159 = (82/159) = 0.5157
The probability that a student passes the test given that he or she took the class = P(A | B) = P(A n B) ÷ P(B) = (82/159) ÷ (115/159)
[tex]\begin{gathered} P(A|B)=\frac{82}{159}\div\frac{115}{159} \\ =\frac{82}{159}\times\frac{159}{115} \\ =\frac{82}{115} \end{gathered}[/tex]P(A | B) = (82/115)
Hope this Helps!!!
