Question

Consider a gene with four alleles a1, a2, a3, and a4. if the cross a1a2 × a3a4 yields two offspring, what is the probability that both of them have the same genotype?

Answer 1

Possible genetic combinations of offspring are:

- A1A3
- A2A3
- A1A4
- A2A4


Therefore, each genotype has a probability of 1/4

The probability of having thesame genotype the second time is 1/4 * 1/4

= 1/16

The probability that both offsprings will have the same genotype is 1/16

Answer 2

The probability of off springs that both of them have the same genotype is $\boxed{\frac{{\mathbf{1}}}{{\mathbf{4}}}}$ .

Further explanation:  

Probability is defined as the ratio of the number of favorable outcome by the total number of outcomes.

Genotype is the collection of genes of an organism that is responsible for the various genetic traits.

Given:

It is given that there are four alleles ${a_1},{a_2},{a_3},{a_4}$ . A person has two off springs.

Step by step explanation:

Step 1:

The two off springs have this genotype ${a_1}{a_2}\times{a_3}{a_4}$ .

The possible genetic combination of offspring are,

${A_1}{A_3},{A_2}{A_3},{A_1}{A_4},{A_2}{A_4}$

It can be seen that there is total outcome is 4 and the favorable outcome is 1.

Therefore, the probability of each genotype is $\frac{1}{4}$  

Step 2:

If the probability of one offspring is $\frac{1}{4}$ .

Then the probability of second offspring is also $\frac{1}{4}$ .

Therefore, the probability of off springs that both of them have the same genotype is $\frac{1}{4}$ .

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Probability

Keywords: genotype, off springs, probability, genes, second offspring, first offspring, genetic, combination, possibility, favorable outcome, collection, organism, traits, total outcome.