A book has n typos. Two proofreaders, Prue and Frida, independently read to book. Prue catches...

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A book has n typos. Two proofreaders, Prue and Frida, independently read to book. Prue catches each typo with probability p₁ and misses it with probability q₁ = 1 p₁, independently, and likewise for Frida, who has probabilities p₂ of catching and q = 1-p2 of missing each typo. Let X₁ be the number of typos caught by Prue, X2 be the number caught by Frida, and X the number caught by at least one of the proofreaders. a. Find the distribution of X. b. Assume that p₁ = p2. Find the conditional distribution of X1 given that X₁ + X₁ = t. A book has n typos. Two proofreaders, Prue and Frida, independently read to book. Prue catches each typo with probability p₁ and misses it with probability q₁ = 1 p₁, independently, and likewise for Frida, who has probabilities p₂ of catching and q = 1-p2 of missing each typo. Let X₁ be the number of typos caught by Prue, X2 be the number caught by Frida, and X the number caught by at least one of the proofreaders. a. Find the distribution of X. b. Assume that p₁ = p2. Find the conditional distribution of X1 given that X₁ + X₁ = t.