Approximately 80,000 marriages took place in the state of New York last year. Estimate the probability that for at least one of these couples, (a) both partners were born on April 30; (b) both partners celebrated their birthday on th

Answer:a)0,45119b)1Step-by-step explanation: For part A of the problem we must first find the probability that both people in the couple have the same birthday (April 30)[tex]P=\frac{1}{365} *\frac{1}{365}=\frac{1}{133225} \\[/tex]Now the poisson approximation is usedλ=nP=80000*1/133225=0,6Now, let X be the number of couples that birth April 30P(X ≥ 1) = 1 − P(X = 0) =[tex]1-\frac{(e^-0.6)*(-0,6)^{0} }{0!}[/tex]P(X ≥ 1) = 0,45119B)  Now want to find the probability that both partners celebrated their birthday on th, assuming that the year is 52 weeks and therefore 52 thursday[tex]P=52*\frac{1}{365} *\frac{1}{365}=\frac{52}{133225} \\[/tex]Now the poisson approximation is usedλ=nP=80000*52/133225=31.225Now, let X be the number of couples that birth same dayP(X ≥ 1) = 1 − P(X = 0) =[tex]1-\frac{(e^-31.225)*(-31.225)^{0} }{0!}[/tex]P(X ≥ 1) = 1