Answer:
a. P(A∪B)=0.85
b. P(A∩C)=0
c. P(A/B)=0
d. P(B∪C)= 0.70
Step-by-step explanation:
Events are said to be mutually exclusive when both cannot occur simultaneously in the result of experimentation. They are also known as incompatible events.
Being P(A)=0.30, P(B)= 0.55 and P(C)= 0.15
Let A and B be any two events, P (A) and P (B) the probability of occurrence of events A or B, is known as the probability of union [denoted as P (A U B)]:
P(A∪B)=P(A) + P(B) - P(A∩B)
Mutually exclusive events are results of an event that cannot occur at the same time. So:
P(A∩B)=0 That is, there is no chance that both events will occur.
So: P(A∪B)=P(A) + P(B)
In this case: P(A∪B)=P(A) + P(B)= 0.30 + 0.55 → <u><em>P(A∪B)=0.85</em></u>
As mentioned, if two events are mutually exclusive, there is no chance that both events will occur. Being the intersection an operation whose result is made up of the non-repeated and common events of two or more sets, that is, given two events A and B, their intersection is made up of the elementary events that they have in common, then: <u><em>P(A∩C)=0</em></u>
The probability that event A will occur if event B has occurred is called the conditional probability and is defined:
P(A/B)=P(A∩B)÷P(B) being P(B)≠0
Since A and B are mutually exclusive, P (A∩B) = 0. So:
P(A/B)=P(A∩B)÷P(B)=0÷0.55 → <u><em>P(A/B)=0</em></u>
Finally, P(B∪C)=P(B) + P(C) - P(B∩C)
Since A and B are mutually exclusive, P (B∩C) = 0. So:
P(B∪C)=P(B) + P(C)= 0.55 + 0.15 → <u><em>P(B∪C)= 0.70</em></u>
