Finding Probability in Genetics Experiment: Vermillion Eyes or Miniature Wings?

  • Thread starter meowmix
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In summary, the probability of a fly having either vermillion eyes or miniature wings is 16/30, and the probability of that not being true is 8/15.
  • #1
meowmix
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I suck at probability. I can't think of ways of understanding any problems that involve probability. Here's the problem I'm currently stuck on:

In a genetics experiment, the researcher mated two Drosophila fruit flies and observed the traits of 300 offspring. The results are shown in the table.
Code:
                WING SIZE
EYE COLOR       Normal    Miniature
Normal          140       6
Vermillion      3         151
What is the probability that the fly has either vermillion eyes or miniature wings, or both?

So the first thing I did was make it a little easier for me to understand by rewriting the table in terms of frequency:
Code:
                WING SIZE
EYE COLOR       Normal    Miniature
Normal          4/15      1/50
Vermillion      1/100     151/300

Now I've thought of a method for going about solving the problem but it doesn't work. Isn't it correct that P(A or B) = P(A) + P(B)? So I figured that the answer would be P(VermillionEyes or MiniatureWings or Both) = P(VermillionEyes) + P(MiniatureWings) + P(Both). That would be 154/300 + 157/300 + 151/300. BUT THIS IS OBVIOUSLY WRONG SINCE IT GOES PAST 300/300!

How do I do this? Why is the P(A or B) = P(A) + P(B) thing not working?
 
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  • #2
A total of 3+ 151= 154 flies have vermilion eyes (now that I would like to see!) and another 6 flies have minature wings so 154+ 6= 160 flies have "either vermillion eyes or miniature wings, out of 300. The probability of that is 160/300= 16/30= 8/15.

Another way to do that is to say the in order not to have "vermilion eyes or miniature wings or both" a fly must have both normal wings and normal eyes. There are 140 such flies so the probability of that is 140/300= 14/30= 7/15. The probability that that is not true is 1- 7/15= (15-7)/15= 8/15 again.

Your mistake is in saying "(VermillionEyes or MiniatureWings or Both) = P(VermillionEyes) + P(MiniatureWings) + P(Both)"

The correct formula is (VermillionEyes or MiniatureWings or Both) = P(VermillionEyes) + P(MiniatureWings) - P(Both). Do you see the minus sign? The reason is that "vermilion eyes" includes "minature wings" and "miniature wings" includes "vermilion eyes". P(Vermilion eyes) and P(MinatureWings) includes both twice. You need to subtract one of them, not add it in again!
 
  • #3
Thanks HallsOfIvy your explanation was very helpful and clear.
 
  • #4
dude, u don't suck at all, because u understood it right away when others explained it to u , a bit more practice and u will be fine! =]
 

1. What is the purpose of finding probability in a genetics experiment?

The purpose of finding probability in a genetics experiment is to determine the likelihood of a certain trait or characteristic appearing in a population. This information can be used to predict the outcomes of breeding experiments and to better understand the inheritance patterns of specific traits.

2. How is probability calculated in a genetics experiment?

Probability in a genetics experiment is calculated using the principles of Mendelian genetics, which involves understanding the inheritance of genes from parents to offspring. The probability of a certain trait appearing is determined by the presence or absence of specific alleles and the chances of these alleles being passed down from parents to offspring.

3. Why are vermillion eyes and miniature wings commonly used in genetics experiments?

Vermillion eyes and miniature wings are commonly used in genetics experiments because they are easily observable traits with distinct variations. These traits are also controlled by a single gene, making them ideal for studying the principles of inheritance and probability.

4. How does the sample size affect the accuracy of the probability in a genetics experiment?

The sample size plays a crucial role in determining the accuracy of probability in a genetics experiment. A larger sample size increases the reliability of the results and decreases the margin of error. This is because a larger sample size represents a more diverse and representative population, leading to more accurate predictions of trait probabilities.

5. Can probability in genetics experiments be affected by other factors besides genetics?

Yes, probability in genetics experiments can also be affected by environmental factors, such as temperature, nutrition, and exposure to toxins. These external factors can influence the expression of certain genes and ultimately affect the probability of a specific trait appearing in a population.

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