###### >Episode 2: Hardy and Weinberg to the rescue

## Finding q

After escaping the OA by saying he had work to do, the Assistant slipped into his office. He had just started to play a game of hangman when the phone rang. “Get down to the Swedish Hospital and Hair Academy ,” roared the ME. "It seems that blue-hair syndrome has appeared there as well. A full 40% of the patient population has blue hair. The Academy would like to “I'm on it like a blue light special,” promised the Assistant. |

Just by observing a population, you can't tell how many carriers there are, but you **can** tell how common the homozygous recessives are (in this case, blue-haired people).

So, is it possible to determine the actual prevalence of an allele (i.e., the value of p) if you only know the how many recessive phenotypes are out there? (This being a math module, obviously the answer is yes...)

### What is q, assuming that 40% of the population shows the recessive trait?

(To make this problem interactive, turn on javascript!)

- I need a hint ... : What proportion of the population exhibits the recessive trait, in terms of p and q?

- ...another hint ... : Since q
^{2}is the proportion of the population exhibits the recessive trait, and q^{2}= 40%, what mathematical operation would allow you to find q? - ...If you get a number that's much too small... : You need to express 40% as a number between 0 and 1 (a proportion).

The problem is that percentages are really fractions, so taking a square root is not simple -- you can tell that the answer is wrong if q is way too low, like 6%.

#### I think I have the answer: Square root(.40) = 0.63

### How common are carriers, assuming that 40% of the population shows the recessive trait?

(To make this problem interactive, turn on javascript!)

- I need a hint ... : You already found q in the last problem (0.63).

- ...another hint ... : If you know q, you can also find p...

#### I think I have the answer: 2*0.37*0.63 = 0.47, or 47%

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