a) "X=" the number of days when Patty goes to class: "X\\sim B(n, p)"
Given that "n=5, p=0.2"
Find the probability that in a given week (5 days), Patty goes to class at least once.
"=1-\\binom{5}{0}0.2^0(1-0.2)^{5-0}=0.67232"
b) "X="the number of days until Patty goes to class for the first time: "X\\sim Geom(p)"
Given that "p=0.2"
c) "X=" number of days until "r^{th}" day Patty goes to his class: "X\\sim NegBin(r, p)"
Given that "r=3, p=0.2"
"P(X=84)=\\binom{84-1}{3-1}(1-0.2)^{84-3}0.2^3\\approx0.0000003848"
d) "X=" days when Patty goes to class in a given week (5 days):: "X\\sim B(n, p)"
Given that "n=5, p=0.2"
Find the probability that in a given week (5 days), Patty goes to class less than two times
"=\\binom{5}{0}0.2^0(1-0.2)^{5-0}+\\binom{5}{1}0.2^1(1-0.2)^{5-1}="
"=0.32768+0.4096=0.73728"
Find the probability that he doesnot get a doughnut until the fourth week.
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