Simple Statistical Question

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In summary, the probability of having two children with the same appearance and sex is 0.5 for both blue and green eyes. The probability for having two children with the same appearance and opposite sexes is 0.5 for both blue and green eyes.
  • #1
jaxnnux
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Hello Gentlemen,

Here's a statistical question for you:

A man and a woman mate to produce a child that either has blue eyes (B) or green eyes (b), where blue eyes are dominant to green eyes.

As you remember from biology, there are 3 different possibilities for the genotype - BB, Bb, or bb.

The probabilities are 1:2:1 for BB:Bb:bb.

Thus, the chance for the child to have blue eyes is 3/4 and green eyes is 1/4.

Ok, I'm getting to the question now. The couple decides to have 2 children. What is the probability that the 2 children will have the same appearance and be of the same sex?

Here's what I think the answer is:

green eyes: (0.5*0.5*0.25*0.25)*100% = 1.5%
blue eyes:
(0.5*0.5*0.75*0.75)*100% = 14.1%

Is this correct? Thanks.
 
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  • #2
Prob(same sex) = P(boy)2+P(girl)2 = 2(0.5)2 = 2*0.25 = 0.5.

Blue boys = (0.5*0.75)2 = Blue girls

green boys = (0.5*0.25)2 = green girls

Blue boys or blue girls = 2(0.5*0.75)2
green boys or green girls = 2(0.5*0.25)2
 
  • #3


I cannot confirm whether your calculations are correct without knowing the exact values of each variable used. However, the general approach you have taken seems to be correct. In order to determine the probability of both children having the same appearance and sex, we need to consider the probability of each combination of genotype and sex. For example, the probability of both children having blue eyes and being male (BB, BB) would be (0.75*0.75)*100% = 56.25%. Similarly, the probability of both children having green eyes and being female (bb, bb) would be (0.25*0.25)*100% = 6.25%. By summing up the probabilities of all possible combinations, we can arrive at the overall probability of both children having the same appearance and sex. I would recommend double-checking your calculations and using specific values for each variable to ensure accuracy.
 

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A simple statistical question is a question that can be answered using basic statistical methods and does not require complex calculations or advanced statistical techniques.

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