If a and b are independent events with p(a) = 0.05 and p(b) = 0.65, then the conditional probability p(a |
b. is

Two events are said to be independent when the occurence of one event does not in any way affects the occurence of the other event.

For independent events, the probablilty of event A happening given that event B has happened is given by the probability of event A happening.

i.e. P(a | b) = P(a).

Therefore, given that p(a) = 0.05 and P(b) = 0.65, then p(a | b) = p(a) = 0.05.

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