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bushindo

Member Since --
Offline Last Active Feb 04 2014 08:32 PM
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Topics I've Started

Blue eyes and green eyes

29 March 2013 - 07:28 PM

Let's say that in a certain country, there are two types of people- blue-eyed and green-eyed. 
 
Let's assume that eye color are governed by a single gene, which can be in the dominant form (B) or recessive form (g).  This means that people in this country have the genotype BB (blue-eyed), Bg (blue-eyed), or gg (green-eyed). The relative frequency of these genotypes in the population is BB (50%), Bg (25%), and gg( 25%).
 
Judy (blue-eyed) is married to Jack (blue-eyed). Judy's parents are both blue-eyed; one of Jack's parents is blue-eyed while the other is green-eyed. Judy and Jack's first child has blue eyes.
 
1) Given the above, what is the probability that Judy's father has the dominant genotype BB?
2) What is the chance that Judy and Jack's second child is green-eyed?

More divisibility

12 February 2013 - 12:11 AM

This is an extension of Prime's excellent puzzle One's Divisibility

 

What is the smallest 101-plus-digit number consisting of only 4's, 5's, and 7's that is divisible by '7777.....777' (one hundred 7's)?

 

The solution *must contain* at least one 4, one 5, and one 7.

 

EDIT: clarified the properties of the required solution