Asked by Lisa
Jeeves is a butler with 6 bathrooms. He's too busy to clean every bathroom everyday. Instead he randomly chooses a bathroom everyday and cleans it.
1) what is the probability that after 30 days, exactly 1 bathroom has never been cleaned?
2) FUZZY THE CAT COUGHS UP A hairball in the master bedrppm. How long should we expect to wait until jeeves cleans it up?
1) what is the probability that after 30 days, exactly 1 bathroom has never been cleaned?
2) FUZZY THE CAT COUGHS UP A hairball in the master bedrppm. How long should we expect to wait until jeeves cleans it up?
Answers
Answered by
Damon
probability of non clean for each bathroom in each day is 5/6
what is the probability of 1 not clean in thirty trials?
Probability of non clean = 5/6
number of trials 30
Bernoulli (n/k) is binomial coef
p k non cleans in n trials = (n/k)(5/6)^k(1-5/6)^(n-k)
here k = 1 and n=30
(30/1) = 30!/[29!1!] = 30
so probability of exactly one non clean in 30 trials is
30 (5/6)^6 (1/6)^24
what is the probability of 1 not clean in thirty trials?
Probability of non clean = 5/6
number of trials 30
Bernoulli (n/k) is binomial coef
p k non cleans in n trials = (n/k)(5/6)^k(1-5/6)^(n-k)
here k = 1 and n=30
(30/1) = 30!/[29!1!] = 30
so probability of exactly one non clean in 30 trials is
30 (5/6)^6 (1/6)^24
Answered by
Damon
for the second part it is a particular bathroom of the 6
The probability that this bathroom is not cleaned each day is 5/6
after n days the probability is (5/6)^n
how many days until the probability is like 1/2 ?
1/2 = (5/6)^n
log .5 = n log (5/6)
-.301 = n (-.07918)
n = 3.8 days
so the chances are 50/50 that Jeevs got it by the fourth day
The probability that this bathroom is not cleaned each day is 5/6
after n days the probability is (5/6)^n
how many days until the probability is like 1/2 ?
1/2 = (5/6)^n
log .5 = n log (5/6)
-.301 = n (-.07918)
n = 3.8 days
so the chances are 50/50 that Jeevs got it by the fourth day
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