P(A) = 0.3, P(B) = 0.7 (a) Can you compute P(A and B) if you only know P(A) and P(B)?(b) Assuming that events A and B arise from independent random processes, i. what is P(A and B)?ii. what is P(A or B)?iii. what is P(A|B)?(c) If we are given that P(A and B) = 0.1, are the random variables giving rise to events A and B indepen-dent?(d) If we are given that P(A and B) = 0.1, what is P(A|B)?

Answer:Step-by-step explanation:Given that [tex]P(A) = 0.3, P(B) = 0.7[/tex]a) this is not sufficient to calculate P(A and B) unless we know how many entries are common between themb) Assuming that events A and B arise from independent random processes, When A and B are independent joint probability would be the product of probabilitiesi.  P(A and B)? = [tex]P(A)*P(B) = 0.21[/tex]ii.  P(A or B)=[tex]P(A)+P(B)-P(AB)\\= 0.3+0.7-0.21\\= 0.79[/tex]iii.  P(A|B) = P(A) when A and B are independent. c. If we are given that P(A and B) = 0.1, are the random variables giving rise to events A and B independent? No here P(AB) not equals P(A) P(B)So A and B cannot be independent.d. If we are given that P(A and B) = 0.1, P(A|B)=[tex]\frac{P(AB)}{P(B)} \\=\frac{0.1}{0.7} \\=\frac{1}{7}[/tex]