Two species of macaws (blue- & red-tailed) observed by researcher

Hello, Here are some questions and my attempts, can someone kindly guide me.

Problem 1. Bayes Theorem: Species identification

Two species of macaws occupy a patch of forest. Eighty-five percent of the birds are blue-tailed, and 15% are red-tailed. They feed at dawn. A researcher identified a feeding bird as blue. However, at this time of the morning, when light is weak, the researcher identifies correct color 80% of the time and fails 20% of the time. What is the probability that the sighted bird was NOT a blue-tailed macaw?

Raja said:

Hello, Here are some questions and my attempts, can someone kindly guide me. View attachment 9537View attachment 9538View attachment 9539View attachment 9540View attachment 9541View attachment 9542

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Please break these into three different threads.

The first problem is:
Two species of Macaw inhabit a patch of trees. 85% of the birds are blue tailed and 15% are red tailed. They feed at dawn. A researcher identifies a feeding bird as blue. However, at this time of the morning, when light is weak, the researcher identifies the correct color 80% of the time. What is the probability that the sighted bird was NOT a blue-tailed Macaw?

Imagine 1000 Macaws. 85% of them, 850, are blue tailed and 15%, 150, are red tailed. Of the 850 blue tailed Macaws, 80%, 680, are identified as blue tailed and the other 170 are identified as red tailed. Of the 150 red tailed Macaws, 80%, 120, are identified as red tailed and the other 30 are identified as blue tailed. So a total of 680+ 30= 710 Macaws are identified as blue tailed but 30 of them were red tailed. The probability a Macaw identified as blue tailed was actually red tailed is 30/710= 3/71.