Given 2P(A)=P(B)=135
From this:
P(B)=135
2P(A)=135
P(A)=265
Also given: P(A∣B)=52
The conditional probability formula is:
P(A∣B)=P(B)P(A∩B)
Rearranging for P(A∩B):
P(A∩B)=P(A∣B)×P(B)
P(A∩B)=52×135
P(A∩B)=6510
P(A∩B)=132
Therefore, P(A∩B)=132