Answer:
The required probability is 0.8616
Explanation:
Consider the provided information.
It is given that the probability that conditions are perfect is 0.76 and The probability that I catch fish given that fishing conditions are perfect is .84.
Let A is the event represented by conditions are perfect and B is i catch fish.
Thus P(A)=0.76 and P(B|A) = 0.84,
Also, it is given that the probability that I do not catch fish given that fishing conditions are not perfect is .07.
The above statement is converse of P(B|A) so represent it as P(B'|A') = 0.07
According to complement rule:
P(A') = 1-P(A) = 0.24
P(B|A') = 1-P(B'|A') = 1-0.07=0.93
We need to find the probability of catching a fish.
The probability of catching a fish is:
There are two case: If conditions are in favor and i caught a fish, or If conditions are not in favor but still i caught a fish.
P(B)=P(A)×P(B|A)+P(A')×P(B|A')
P(B)= 0.76×0.84+0.24×0.93
P(B)= 0.6384+0.2232
P(B)= 0.8616
Hence, the required probability is 0.8616