Respuesta :
Answer:
a. A and B are disjoint
Step-by-step explanation:
We know that P(A and B)=0, It means that event A and event B have nothing in common and it means that event A and event B are disjoints events.
The event A and event B are independent if
P( A and B)= P(A)*P(B)
P(A)*P(B)=0.3*0.2=0.06
So, P(A and B)≠P(A)*P(B)
Hence events A and B are not independent.
Option a is A and B are disjoints which is correct
Option b is A and B are neither disjoints nor independent which is partially false as A and B are disjoints event.
Option c states that A and B are independent which is clearly false.
Option d states that A and B are disjoints and independent which is partially false as A and B are not independent.
Hence the correct option is option A.
So, option (A) is correct.
Disjoint Probability: If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring that is P(A and B) = 0.
Given that,
[tex]P(A) =0.3\\ P(B) = 0.2 \\P(A or B) = 0.5 \\P(A\cup B)=P(A)+P(B)\\0.5=0.3+0.2\\0.5=0.5[/tex]
Hence, A and B are disjoint to each other.
Learn More about the topic disjoint of the probability:
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