Respuesta :
Answer:
1. The probability that B occurs or A does not occur (or both) is 0.73.
2. The probability that either B occurs without A occurring or A and B both occur is 0.73.
Step-by-step explanation:
It is given that the events A and B are mutually exclusive. It means the intersection of A and B is 0.
[tex]P(A\cap B)=0[/tex]
Given information:
[tex]P(A)=0.02[/tex]
[tex]P(B)=0.73[/tex]
We get,
[tex]P(A')=1-P(A)=1-0.02=0.98[/tex]
[tex]P(B')=1-P(B)=1-0.73=0.27[/tex]
(1) We need to find the probability that B occurs or A does not occur (or both).
[tex]P(B\cup A')+P(A\cap B)=P(B)+0[/tex]
[tex]P(B\cup A')+P(A\cap B)=0.73+0[/tex]
[tex]P(B\cup A')+P(A\cap B)=0.73[/tex]
Therefore the probability that B occurs or A does not occur (or both) is 0.73.
(2) We need to find the probability that either B occurs without A occurring or A and B both occur.
[tex]P(B\cup A')+P(A\cap B)=P(B)+0[/tex]
[tex]P(B\cup A')+P(A\cap B)=0.73+0[/tex]
[tex]P(B\cup A')+P(A\cap B)=0.73[/tex]
Therefore the probability that either B occurs without A occurring or A and B both occur is 0.73.
