Respuesta :
Answer:
a) [tex] p(A) = \frac{2}{5}[/tex]
b) [tex] p(B) =\frac{3}{5}[/tex]
c) [tex] p(A') = 1-p(A) = 1-\frac{2}{5} = \frac{3}{5}[/tex]
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
[tex] P(AUB) = P(A) +P(B) -0 = \frac{2}{5} +\frac{3}{5} =1[/tex]
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:
[tex] S= [a,b,c,d,e][/tex]
And we have defined the following events:
[tex] A= [a,b][/tex]
[tex] B= [c,d,e][/tex]
For this case we can find the probabilities for each event using the following definition of probability:
[tex] p =\frac{Possible cases}{total cases}[/tex]
The total cases for this case are 5 , the possible cass for A are and for B are 3.
Usign this we have this:
[tex] p(A) = \frac{2}{5}, p(B) = \frac{3}{5}[/tex]
Then we can find the following probabilites:
a) P(A)
[tex] p(A) = \frac{2}{5}[/tex]
b) P(B)
[tex] p(B) =\frac{3}{5}[/tex]
c) P(A')
Using the complement rule we have this:
[tex] p(A') = 1-p(A) = 1-\frac{2}{5} = \frac{3}{5}[/tex]
d) P(A∪B)
For this case we can use the total probability rule and we got:
[tex] P(AUB) = P(A) +P(B) -P(A and B)[/tex]
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
[tex] P(AUB) = P(A) +P(B) -0 = \frac{2}{5} +\frac{3}{5} =1[/tex]
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
