Answer:
OPTION A: [tex]$ \frac{11}{20} $[/tex]
Step-by-step explanation:
[tex]$ P(A | B) = \frac{P(A \cap B)}{P(B)} $[/tex]
[tex]$ P(not B) = 1 - P(B) = 1 - \frac{13}{20} = \frac{7}{20} $[/tex]
[tex]$ \implies P(A \cap B)= P(A | B) \times P(B) $[/tex]
[tex]$ = \frac{11}{20} \times \frac{7}{20} $[/tex]
Let us keep it without multiplying for easy simplification later.
Also, let us assume A and B are independent events.
[tex]$ P(A \cap B) = P(A) \times P(B) $[/tex]
[tex]$ \implies \frac{11}{20} \times \frac{7}{20} = P(A) \times \frac{7}{20} $[/tex]
[tex]$ \implies P(A) = \frac{11}{20} $[/tex]
Hence, OPTION A 11/20 is the answer.
