Is meiosis random with an equal chance of genes from either parent?

Question

Is the following simplistic understanding basically corrrect?

A germ cell has 23 chromosomes and at conception comes together with another germ cell. The 23 pairs of chromosomes zip together, matching at alleles. For each gene, either the mother or father’s gene is dominant and expressed in the phenotype of the resulting animal. The other gene at that allele remains unexpressed.

The new being begins meiosis and produces its own germ cells with 23 chromosomes. These chromosomes are new combinations of information, with some information from the father, some from the mother. Gene dominance affects the phenotype, but not meiosis or the composition of chromosomes in the new gamete. Each new chromosome in each gamete is created with a new role of the dice. At every allele there is a 50/50 chance of getting the gene from father or mother, regardless of dominance. Sperm are all unique and any two sperms from one male will on average share about half the same genetic information.

Answer 1

here's the basic math on how it works:

a sperm has exactly half the DNA of the father...which half is random.

and egg has exactly half the DNA of the mother..which half is again random.

So the new being then has EXACTLY half mom and half dad's. Meiosis happens to MAKE the sperm and the egg...so the randomness happens well before the new beign is created

Answer 2

Your summary is excellent.  

Mendel expressed the same things when he established four principles of genetics.  The four basic statements of principles regarding Mendelian genetics were:

1. The Principle of Unit Characters  states that individuals pass information on as individual traits.

2. The Principle of Dominance and Recessiveness states that some unit characters (genes or alleles) can mask the expression of others.

3. The Principle of Segregation states that during gamete formation each of the two alleles for a trait separate into a different s*x cell.

4. The Principle of Independent Assortment states that genes segregate according to chance.

The only thing you missed in your summary was it is possible for two recessive alleles to be a genotype resulting in a recessive phenotype.