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,

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step-by-step explanation:

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i hope i

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!