Probability Calculations for Random Samples and Genetic Inheritance

[brunettegurl]

1) A random sample of 2 people are selected from a group of 15 girls and 8 boys to participate in a study. Find the probability that the sample consists of 1 boy and 1 girl.

My take : n=23 P(1girl)*P(1boy)
(15/23)*(8/23)
= 0.2268
the answer should be 0.4743

2)Suppose that a disease is inherited via an autosomal recessive mode of inheritence.The children in the family have a probability of 1/4 of inheriting the disease. In a family of 4 children, find the probability that at least one of the children inherits the disease.

My take: n=4 x=1 p=1/4
nCx= n!/x!(n-x)! f(x)= nCx* p^x(1-p)^n-x

I get 0.4219
The answer should be 0.6836

Any help would be appreciated.

Thanks

 

[The Investor]

The simplest way to solve these problems:

1) P (1 boy 1 girl) = 1-P(2 girls) - P(2 boys)

2) P(one child or more inherits disease) = 1-P(no child inherits disease)These are very easy to work out, and don't require the level of complexity of the formulas you are using.

 

[brunettegurl]

Thanks!

 

[mathman]

If you want to do the first one directly, you need to do it properly.
girl first boy second = (15/23)(8/22)
boy first girl second = (8/23)(15/22)

Final answer (2x8x15)/(23x22)