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November 17th, 2017, 12:15 AM   #1
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Probabilities- Some consultation

Hey guys I have the following problem:

If the probability is 0.60 that a divorcee will remarry within
three years, find the probabilities that of 5 divorces:

a)At least 3 will remarry within 3 years:

x=3,4,5, Thus: f(3)= log5.C3. (0.60)^3= 0.15
f(4)= log5.C4. (0.60)^4= 0.09
f(5)= log5.C5. (0.60)^5= 0.054
I think my way is correct but I am not sure my calculations are: Can anyone more experienced tell me his opinion: I will be grateful!

b) 3 of 5 divorces will remarry withing 3 years
Here I could use some help if someone can help me. I guess I choose again x=3,4,5 but i'm not sure how should I represent the function.
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November 17th, 2017, 08:20 AM   #2
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This is just a binomial distribution with parameters $n=5,~p=0.6$


$P[\text{at least 3 will remarry within 3 yrs}]=P[\text{3, 4, or 5 remarry within 3 yrs}]=\dbinom{5}{3}(0.6)^3(1-0.6)^{5-3}+\dbinom{5}{4}(0.6)^4(1-0.6)^{5-4}+\dbinom{5}{5}(0.6)^5(1-0.6)^{5-5}$

why you are bringing logs into the picture I don't know. I leave you to work out the final numbers on this.

b) seems to ask the probability of exactly 3 remarrying.

This is (a) without the terms corresponding to 4 and 5 remarrying i.e.

$P[\text{3 remarry within 3 yrs}]=\dbinom{5}{3}(0.6)^3(1-0.6)^{5-3}$
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