Question

Biostatistics,

Problem # 4, is my n=8 or n=2?

3) Mendelian genetics predict that in Labrador retrievers (a type of dog), 25% should have brown coat color if both parents are heterozygous (the rest are black). You mate two parents and get a litter of 8- puppies. Calculate the following: b) The probability of 3 brown puppies. a) The probability of 6 black puppies. c) The probability that 50% of the puppies will be brown. (Comment: You do not need to know anything about genetics to solve this problem. If you're trying to do things like use punnet squares, you're doing things wrong) 4) Refer to problem 3. Calculate the probability of every possible outcome (hint: you need to make nine calculations (you already made three of them in problem 3)). n2

Answer 1

4)

n = 8

Here, you'll be calculating the probability of number of brown puppies in a litter of 8. The general formula is:

Probability of 'x' Brown Puppies =

8C, (Probability of Brown Puppy)" x (Probability of Black Puppy) 8-1

So,

Probability of 0 Brown and 8 Black Puppies =

8- 0 81 *cox ()° () = 3X0 X1X 65536 = 65536 = " 6561 6561

Probability of 1 Brown and 7 Black Puppies =

CX- 8! 2187 7111X 0.25 X 100 16384 = 8 x 0.25 x 2187 16384

4374 = 0.266960.267 16384

Probability of 2 Brown and 6 Black Puppies =

s /11 31 -2 8 1 729 8x71 729 CCSX(1)*(i)=68x21*16*4096 - 2*16*4096

7 x 729 4 x 4096 = 0.31146 0.312

Probability of 3 Brown and 5 Black Puppies =

(13 (38-3 8 2438x7x6 1x 243 *03 * (1) * () = 5! X 3! * 5 * 1024 = 3x2 x 64 x 1024

8 x 7 x 243 -= 0.20764 64 x 1024 0.208

Probability of 4 Brown and 4 Black Puppies =

X C4 X (14 (38–4 8 1 81 4! * 4 256 * 256 -

8 x 7 x 6 x 5 4 x 3 x 2 1 x 81 256 X 256 2 X 7 X 5 X 81 = 0.086517 1 x 256 256 0.087

Probability of 5 Brown and 3 Black Puppies =

8-5 °C5 * G * () 27 8 x 7 x 6 27 = 3! X 51 X 1024 * 54 = 3x2 * 1024 64

8 x 7 x 27 1024 x 64 = 0.023071 0.023

Probability of 6 Brown and 4 Black Puppies =

8-6 81 °C6 x G) *(a) 98x7 1x 9 = 2! X 6! * 4096 * 16 = 2 * 4096 x 16

8 x 7 x 9 2 x 4096 x 16 = 0.0038

Probability of 7 Brown and 1 Black Puppy =

*07*(1) *(*)** - 17 (1 7 138- 7 4) (4) 8! 1 3 8 1x3 1! * 7 * 16384 * 7 =ī* 16384 x 4 = 0.000366

Probability of 8 Brown and 0 Black Puppies =

18 (318-8 8! 1 $C$ * (1) ** () = 0, $ 87 X 65536 * 1=1X 65536 = 0