Question 1185603
Fish can feed near the surface or the bottom of a pond. The probability of a
fish feeding at the surface of a pond is 60%.
- what is the probability of a fish feeding near the bottom of a pond?
100% - 60% = 40%
- are these events mutually exclusive?
"Mutually excluSIVE" is an unfortunate choice of words, though all the textbooks
use it. It should be "Mutually excluDING". When you say "Two events are
mutually exclusive", that means "They EXCLUDE each other". If one event occurs,
the other one cannot occur.
Since we are talking about ONE SPECIFIC fish, then that ONE fish feeding at the
surface EXCLUDES that one fish feeding near the bottom. Since it says "a fish"
and not "some of the fish", then the events are mutually exclusive.
[However, if it had said "some fish", and not "a fish", the events would not be
mutually exclusive because some fish feeding at the surface DOES NOT EXCLUDE
some of the other fish feeding near the bottom.]
- if we observe 3 fish, what is the probability that one will feed near the
surface and two will feed near the bottom of a pond
They are mutually exclusive events. So that's a binomial probability. We will
call a fish feeding near the surface "a success" and a fish feeding at the
bottom "a failure".
Here's the formula:
Substituting:
Edwin