+561 Mr. Wong has 10 grandchildren. Assuming that the gender of each child is determined independently and with equal likelihood of male and female, what is the probability that Mr. Wong has more grandsons than granddaughters or more granddaughters than grandsons?
1) Equal probability of 5 boys and 5 boys =
binomial(5 + 5, 5) 2^(-(5 + 5)) = ((5 + 5)!)/(5! 5! 2^(5 + 5)) = 63/256 ≈ 0.2461 ≈ 1/4.063
(assuming children are independent and male and female are equally likely
2) | probability
less than 5 boys | 0.377
5 or less boys | 0.623
more than 5 boys | 0.377
5 or more boys | 0.623
(assuming children are independent and male and female are equally likely)
+9673 P(more grandsons than granddaughters or more granddaughters than grandsons)
= 1 - P(equal amount of granddaughters and grandsons)
= 1 - \(\left(\dfrac{1}{2}\right)^{10}\)
= \(\dfrac{1023}{1024}\)
By looking at the question, there are clues that you come from China too(Mr WONG!?!?IS IT ME???? LOL). Where you from? Me from Hong Kong.
1) Equal probability of 5 boys and 5 boys =
binomial(5 + 5, 5) 2^(-(5 + 5)) = ((5 + 5)!)/(5! 5! 2^(5 + 5)) = 63/256 ≈ 0.2461 ≈ 1/4.063
(assuming children are independent and male and female are equally likely
2) | probability
less than 5 boys | 0.377
5 or less boys | 0.623
more than 5 boys | 0.377
5 or more boys | 0.623
(assuming children are independent and male and female are equally likely)
+9673 OK....... What is that!?!?
binom of (5+5, 5) thing!?!?
I just treated it as a simple probability problem!!
+561 binomial(5+5,5) is binomial(10,5) and Can also be written as:
10C5
(n,r)C(10,5)......I think that is how u can write it.
it means:
(n!)/(((n-r)!)r!)
so in this case it is:
10!/((10-5)!*5!)
10!/(5!*5!)
(10*9*8*7*6)/(5*4*3*2)
(9*2*7*2) = 252
In words it means you have n things and how many ways can u choose r things out of the n.
FYI n and r are variables.
Here is more in better detail AND LaTeX than me
No Max: Probability can get very complicated very quickly:
The probability of having 5 boys and 5 girls is computed as follows:
10! /[ 5! x 5! x 2^10] =0.24609375 x 100 =~24.61%
+118687 Mr. Wong has 10 grandchildren. Assuming that the gender of each child is determined independently and with equal likelihood of male and female, what is the probability that Mr. Wong has more grandsons than granddaughters or more granddaughters than grandsons?
1 - (probability of 5 girls and 5 boys)
10C5(0.5)^5*(0.5)^5 = 10C5*(0.5)^10 = 0.24609375
1-0.24609375 = 0.75390625 = 75%
