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November 17th, 2017, 12:15 AM  #1 
Newbie Joined: Nov 2017 From: Bulgaria Posts: 3 Thanks: 0  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. 
November 17th, 2017, 08:20 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,091 Thanks: 1087 
This is just a binomial distribution with parameters $n=5,~p=0.6$ a) $P[\text{at least 3 will remarry within 3 yrs}]=P[\text{3, 4, or 5 remarry within 3 yrs}]=\dbinom{5}{3}(0.6)^3(10.6)^{53}+\dbinom{5}{4}(0.6)^4(10.6)^{54}+\dbinom{5}{5}(0.6)^5(10.6)^{55}$ 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. $P[\text{3 remarry within 3 yrs}]=\dbinom{5}{3}(0.6)^3(10.6)^{53}$ 

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