Answer:
a)0,45119
b)1
Step-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 used
λ=nP=80000*1/133225=0,6
Now, let X be the number of couples that birth April 30
P(X ≥ 1) =
1 − P(X = 0) =
[tex]1-\frac{(e^-0.6)*(-0,6)^{0} }{0!}[/tex]
P(X ≥ 1) = 0,45119
B) 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 used
λ=nP=80000*52/133225=31.225
Now, let X be the number of couples that birth same day
P(X ≥ 1) =
1 − P(X = 0) =
[tex]1-\frac{(e^-31.225)*(-31.225)^{0} }{0!}[/tex]
P(X ≥ 1) = 1
