Statistics Overload! Need Help

[nenaquetuhace]

I received a couple of problems but did not know how to solve this one:

Let B be event "butterfly" and M be event "moth". If B and M are the mutally exclusive events that a biologist will catch a butterfly or a moth in a field, P(B) = 0.43, and P(M) = 0.21, find the probabilities that a biologist will
a) not catch a butterfly
b) catch a butterfuly or a moth
c) not catch a butterfly or a moth

Is there any particular way that I could break this problem down in order to solve it.

Thanks

 

[chrisr]

Yes,

the probability he will catch a butterfly is 0.43,
so the probability he will not catch a butterfly is 1-0.43,
since he will either catch a butterfly or not (assuming "catch a butterfly" means "catch at least 1 of them"),
both probabilities must sum to 1, since the percentages sum to 100% (p=0.43 means a 43% chance).

Since the events are mutually exclusive then you can interpret "or" as "sum the probabilities",
since there are at least two ways that part (b) can be labelled a success.
However, there is a third way...
He can catch a butterfly and a moth.
There are therefore 3 ways he can catch a butterfly or a moth.


Then you should be able to decipher (c).

 

[nenaquetuhace]

so the b would be catch a butterfly or moth 0.43 + 0.21= 0.64 64%
and c would be not to catch a butterfly or moth 1.00 - 0.64 = 0.36 36%

 

[chrisr]

The missing piece is ...

the probability he will catch a butterfly and a moth is 0.43(0.21),

so the probability he will not catch a butterfly or moth is 1-{0.64+0.43(0.21)}.