At my favorite fishing hole, the probability that conditions are perfect is. 76. The probability that I catch fish given that fishing conditions are perfect is. 84. The probability that I do not catch fish given that fishing conditions are not perfect is. 07. Use this information to answer the following two questions. What is the probability of catching a fish?

The required probability is 0.8616

Step-by-step 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