Question

1. In a certain forest, the probability that a tree is a red oak is 0.2, and the probability that a tree is a white oak is 0.4. The probability that a tree has mistletoe is 0.20, and the probability that a tree is a white oak and has mistletoe is 0. If a tree is selected at random, what is:
   1. the probability that it is a white oak or it has mistletoe?
   2. the probability that it is not a white or red oak?

Answer 1

Given,

The probability that a tree is a red oak is 0.2,

The probability that a tree is a white oak is 0.4.

The probability that a tree has mistletoe is 0.20,

The probability that a tree is a white oak and has mistletoe is 0 i.e There are no white oak trees in the forest that has mistletoe or in probability terms these two are disjoint event Hence, P( white oak and it has mistletoe ) = 0

Thus we can say that these are mutually exclusive event

A) P(  white oak or it has mistletoe ) = P( white oak ) + P ( it has mistletoe ) - P( white oak and it has mistletoe )

= 0.4 + 0.20 - 0

= 0.60 :ans

B) A tree can not be white oak and red oak at the same time Hence, P( white oak and red oak ) = 0

P( not a white or red oak ) = 1 - P( white or red oak ) = 1 - {P( white oak) + P( red oak ) - P( white oak and red oak) }

= 1 - { 0.4 + 0.2 } = 0.4 : ans