Math/ genetics Q

Started by prsndwg
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prsndwg

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The probability of flipping 3 coins simultaneously and getting 2 tails and 1 head is?

edit: the answer is 1/16 as the answer key shows!!!
 
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The probability of flipping 3 coins simultaneously and getting 2 tails and 1 head is?

The probability of one of these events independantly is 1/2. You then use the product rule which is multiply the probabilities of each individual event by each other.

(1/2)(1/2)(1/2) = 1/8

1/8 is the chance (individual probability) for one outcome of this coin flipping (HHH, HTH, TTH, etc.)

The probability of coints being flipped in any one of these 8 orders = the sum of individual probabilities.

1/8 + 1/8 + 1/8 = 3/8

The probabiliy of this happening is 3/8.
 
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and to the OP... since when is probability and statistics consider genetics?...

I'm not the OP but... Inheritance problems sir.

Taken from my genetics notes:

probability.jpg
 
why there is a 1/4 on the 3rd order?

The 1/4 could just as well been on the 2nd order as the 3rd order. This is just one of the X possibilities for an order including 3 normal & 1 PKU offspring.

And the picture above didn't come from my notes. I don't think gamete frequencies were part of this problem so I'm assuming this problem requires hardy-weinberg equilibrium? Otherwise with those gamete frequencies, 1/4 of the population would not be PKU.
 
I'm not the OP but... Inheritance problems sir.

Taken from my genetics notes:

probability.jpg
You never said what the probability of having PKU actually is. Is it a 1/4 chance? Just because you are looking for 1/4 of the children to have it doesn't mean that 1/4 is the probability.

Going by the standard Punnett square perhaps it is, but you would want to make a note of that. If there were 5 children then you'd have a better example.

prsndwg: The probability of being normal is 3/4 (apparently, see note above). The probability of having PKU is 1/4. So in 4 children, the probability of ANY one and ONLY one of them having the disease is (3/4)(3/4)(3/4)(1/4). Avery07 just put the 1/4 in the third position.

Edit: Okay you put up a Punnett square with different probabilities. You have to use those and not 3/4, 1/4.
 
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The equation for an "exactly x out of y times" question is something like
nCr p^i q^(n-r)
where p is your favored outcome, q is your unfavored outcome, r is your favored frequency. nCr represents the number of such combinations allowed

For a 3-pick-2 question, it will be
3C2 (.5^2)(.5^1)
or
3(1/2)(1/2)(1/2)

In another example: You throw a die 10 times. what is the probability that it will land on "3" exactly 2 times?
The probability of a 3 landing is 1/6, and the probability of not landing is 5/6. The probability then is: 10C2 (1/6)^2 (5/6)^8