Question

I need to see if I did correctly. I am stuck at the last part.

Answer 1

Lets make a contegency table for our problem:

Then , the probability that it is a female or a sky blue parakeet is

`P(\text{female U sky blue)=P(female)+P(sky blue)-P(female n sky blue)}`

where the last probabilbity is given by the intersection of female and sky blue. From our contegency table, we get

`\begin{gathered} P(\text{female U sky blue)=}P(\text{female)+P(sky blue)-P(female n sky blue)} \\ P(\text{female U sky blue)=}(42)/(79)+(44)/(79)-(28)/(79) \end{gathered}`

where 79 is the grand total (21+14+16+28).

This last result comes from the general formula for the union of 2 events:

`\begin{gathered} P(\text{AuB)}=P(A)+P(B)-P(\text{AnB)} \\ \end{gathered}`

we can see that this formula works in the following Venn diagram:

the union of A and B consist in the 3 zones but when you compute the probability you must subtract the intersection zone (AnB) in order to get the correct result because If you not substract this zone you are counting twice the elements in this zone.

Then, the answer is