P(a) = 0.3, p(b) = 0.7 (a) can you compute p(a and b) if you only know p(a) and p() 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|) 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)?

(a) No, we can't compute P(A and B) because we don't know the A and B are independent or not. Also If it not independent we don't know the value of P(A or B)

(b) (i) If A and B are independent then,

P(A and B) = P(A) × P(B)

⇒ P(A and B) = 0.3 × 0.7 = 0.21

(ii) By, Additional theorem of Probability,

P(A or B) = P(A) + P(B) - P(A and B)

⇒ P(A or B) = 0.3 + 0.7 - 0.21 = 0.79

(iii) P(A|B) = P(A) = 0.3

(c) For the events to be independent, it should follow:

P( A and B) = P(A) × P(B)

0.1 = 0.3 × 0.7

⇒ 0.1 ≠ 0.21

Thus, A and B are not independent event.

(d) By the Conditional Probability definition, we know that,

439400

step-by-step explanation:

130^2 = 16900

16900*26 = 439400

yes

step-by-step explanation: