Answer:
(a) No
(b) Yes
Step-by-step explanation:
It is provided that:
P (A) = 0.30
P (B) = 0.40
P (A ∪ B) = 0.70
Compute the value of P (A ∩ B) as follows:
P (A ∩ B) = P (A) + P (B) - P (A ∪ B)
[tex]=0.30+0.40-0.70\\=0[/tex]
(a)
If events X and Y are independent then,[tex]P(X\cap Y)=P(X)\times P(Y)[/tex].
Check whether A and B are independent or not as follows:
[tex]P(A\cap B) = 0\\P(A)\times P(B)=0.30\times0.40=0.12[/tex]
[tex]P(A\cap B) \neq P(A)\times P(B)[/tex]
Thus, the events A and B are not independent.
(b)
If events X and Y are mutually exclusive then,[tex]P(X\cap Y)=0[/tex].
Check whether A and B are mutually exclusive or not as follows:
[tex]P(A\cap B) = 0[/tex]
Thus, the events A and B are mutually exclusive.
