Could someone tell me if my logic for the following probability question is correct?
A scientific experiment has been under taken to evaluate the feeding habits of a new species of parrot in a forest bird population. The probabilities for each nut is independent.
+----------------------+-------------------------+-------------------------------------+
| Nut Type | # Nuts Eaten by Parrot | # Nuts Eaten by Other Birds Species |
+----------------------+-------------------------+-------------------------------------+
| Peanuts | 46 | 20 |
| Walnuts | 25 | 80 |
| Pecan | 63 | 52 |
| Almonds | 10 | 75 |
| Total Nuts Evaluated | 350 | 550 |
+----------------------+-------------------------+-------------------------------------+
I am asked to evaluate $P(Almonds|!Parrot)$ and $P(Peanuts|Pecan)$.
I am confused, would $P(Almonds|!Parrot) = 75/550 = 0.136$ in this case? Or is $0.136$ just $P(!Parrot \wedge Almond)$?
It is $P(\text{almond | not parrot})$.
$P(\text{almond and not parrot})=\frac{75}{350+550}$, that is the denominator have to consider both types of birds.