An urn has n 3 green balls and 3 red balls. Draw l balls with replacement....

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An urn has n– 3 green balls and 3 red balls. Draw l balls with replacement. Let B denote the event that a red ball is seen at least once. Find PB) using the following methods. (a) Use inclusion-exclusion with the events A, = (ith draw is red) Hint. Use the general inclusion-exclusion formula from Fact 126 and the binomial theorem from Fact D.2. (b) Decompose the event by considering the events of seeing a red ball exactly k times, with k = 1,2.…....l (c) Compute the probability by considering the complement B. An urn has n– 3 green balls and 3 red balls. Draw l balls with replacement. Let B denote the event that a red ball is seen at least once. Find PB) using the following methods. (a) Use inclusion-exclusion with the events A, = (ith draw is red) Hint. Use the general inclusion-exclusion formula from Fact 126 and the binomial theorem from Fact D.2. (b) Decompose the event by considering the events of seeing a red ball exactly k times, with k = 1,2.…....l (c) Compute the probability by considering the complement B.