Mathematics: 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 independent? d. if we are given that p(a and b) = 0.1, what is p(a|b)?

P(a) = 0.3, p(b) = 0.7 a. can you compute p(a

SsjDavid

15.01.2022

Step-by-step explanation:

Given that

P(A) = 0.3, P(B) = 0.7

a) this is not sufficient to calculate P(A and B) unless we know how many entries are common between them

b) Assuming that events A and B arise from independent random processes,

When A and B are independent joint probability would be the product of probabilities

i. P(A and B)? = P(A)*P(B) = 0.21

ii. P(A or B)= $P(A)+P(B)-P(AB)\\= 0.3+0.7-0.21\\= 0.79$

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)= $\frac{P(AB)}{P(B)} \\=\frac{0.1}{0.7} \\=\frac{1}{7}$

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