Muggle-born Statistics

[OliveOil_Med]

I have a Harry Potter-related math question for those who are brave enough to venture.

Let's assume that the gene that creates a Muggle-born child is a carrier recessive gene that needs the child to have both recessive genes in order with be born with magic. That being said, the chances of two carrier parents having a magical child is 1/4.

Now, that being said, what would be the chances of a pair of carrier parents having five children, all born with magical abilities?

Brownie points if you can show your work!

[DracoGurlFurever]

It's approximately 0.098 percent (0.098%)

The way you would do the math is as follows:

The chance of the parents having one magical child is 1/4, or 0.25.
The probability that they will have another magical child is unaffected by the probability that their first child was magical (it doesn't matter - in either case, the probability is still 0.25).
Stretching this logic to five children, we can say that, to have 5 magical children in a row, this needs to happen: 0.25 * 0.25 * 0.25 * 0.25 * 0.25 = 0.00097656, or approximately 0.098%.

Hope that helped!

Apurva.

[ahattab33]

I'm only an accountant, not a math major, so somebody who deals in statistics might want to step in an correct my logic....

As far as I know, you would evaluate the chance of each child being born magical separately, and simply multiply those chances together...does that make sense?

Child - Wizard = 25%

Each child has an equal chance every time; that is, for each pregnancy, there is a 25% chance that the child will be born a wizard/witch.

As there are five children being evaluated, that is:

25% x 25% x 25% x 25% x 25% = 0.10%

Make sense? I have no idea if that is correct, but from my slight grasp on my high school algebra, that's correct. As all five are the same characteristic, you aren't concerned about the order in which it appears (which complicates things more).

Someone else should corroborate this, but I hope it helps!

EDIT - Apurva said the same thing. Awesome. And:

Originally posted by Apurva:
The probability that they will have another magical child is unaffected by the probability that their first child was magical

is what I was hinting at, but couldn't say.

[OliveOil_Med]

Wonderful! Thank you very much, you two lovely math geniuses, you! This is exactly what I needed.

What for? Oh, that's a secret!