Each of the possible five outcomes of a random experiment is equally likely. the sample space is {a, b, c, d, e}. all outcomes are equally likely. let a denote the event {a, b}, and let b denote the event {c, d, e}. determine the following probabilities:
a) p(a)
b) p(b)
c) p(a')
d) p(a∪b)
e) p(a∩b)

a)

b)

c)

d) The probability for intersection on this case is 0 because the sets A and B not have any element in common, so then we have this

e) The intersection for this case is the empty set between the sets A and B so for this reason the probability is 0

P(A∩B)=0

Step-by-step explanation:

For this case we have the following sample space:

And we have defined the following events:

For this case we can find the probabilities for each event using the following definition of probability:

The total cases for this case are 5 , the possible cass for A are and for B are 3.

Usign this we have this:

Then we can find the following probabilites:

a) P(A)

b) P(B)

c) P(A')

Using the complement rule we have this:

d) P(A∪B)

For this case we can use the total probability rule and we got:

The probability for intersection on this case is 0 because the sets A and B not have any element in common, so then we have this

e) P(A∩B)

The intersection for this case is the empty set between the sets A and B so for this reason the probability is 0

P(A∩B)=0