My Math Forum permutation and combination

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 June 7th, 2012, 01:37 PM #1 Newbie   Joined: May 2012 Posts: 9 Thanks: 0 permutation and combination ratio male to female is 0.53 . family of 7 children i-what is the probability that all(7) children are boy ii-are girl iii-5 girls , 2 boys thank you
June 7th, 2012, 03:08 PM   #2
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Re: permutation and combination

Hello, talo0000!

Quote:
 Ratio of male to female is 0.53.

$\text{Ratio of Males to Females: }\:53\,:\,100$

$\text{Hence: }\:\begin{Bmatrix}P(M)=&\frac{53}{153} \\ \\ \\ P(\text{F})=&\frac{100}{153} \end{Bmatrix}=$

Quote:
 There is a family of 7 children. (a) What is the probability that all 7 children are boys?

$P(\text{7 M}) \;=\;\left(\frac{53}{153}\right)^7$

Quote:
 (b) all girls?

$P(\text{7 F}) \;=\;\left(\frac{100}{153}\right)^7$

Quote:
 (c) 5 girls, 2 boys

$P(\text{2 M, 5 F}) \;=\;{7\choose2}\left(\frac{53}{153}\right)^2\left (\frac{100}{153}\right)^5$

 June 7th, 2012, 05:39 PM #3 Math Team   Joined: Apr 2012 Posts: 1,579 Thanks: 22 Re: permutation and combination Talo0000, did you mean that there are 53 males for every 100 females or that 53 out of 100 children are male?
 June 8th, 2012, 06:47 AM #4 Newbie   Joined: May 2012 Posts: 9 Thanks: 0 Re: permutation and combination thank you for your quick response but the relation is for every 100 case 53 male and 47 female , usually the relation is one-to-one , but for this special case is .53 to .47
June 8th, 2012, 02:32 PM   #5
Math Team

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Re: permutation and combination

Quote:
 Originally Posted by talo0000 thank you for your quick response but the relation is for every 100 case 53 male and 47 female , usually the relation is one-to-one , but for this special case is .53 to .47
Use the same formulae and just change the raw probabilities used. So, all seven are boys would be .53^7 All seven are girls would be .47^7, etc

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