EK bio lecture 9 #205 genetics question

[slz1900]

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Colorblindness is sex linked recessive. If a colorblind man and a heterozygous female have two boys and two girls, what's the probability that at least one of the girls will be colorblind?

A) 0%
B) 50%
C) 75%
D) 100%

Answer: C

Wut 😕

If you draw out a punnet square, one of the girls is heterozygous and the other is colorblind, which is 50%. EK says 75% because there's a 50% chance that one is colorblind, so there's a 25% chance that both are, therefore 75%. If this is how you calculate phenotypic probabilities, doesn't that mean that punnett squares always underestimate the number of phenotypes in a population? Is this question unique because they say at least 1?

Edit: I get that you have two crosses and each is independent so it's a 50% probability of having a color blind girl each time, but I still don't get how they reached 75%

 

[Postictal Raiden]

Colorblindness is sex linked recessive. If a colorblind man and a heterozygous female have two boys and two girls, what's the probability that at least one of the girls will be colorblind?

A) 0%
B) 50%
C) 75%
D) 100%

Answer: C

Wut 😕

If you draw out a punnet square, one of the girls is heterozygous and the other is colorblind, which is 50%. EK says 75% because there's a 50% chance that one is colorblind, so there's a 25% chance that both are, therefore 75%. If this is how you calculate phenotypic probabilities, doesn't that mean that punnett squares always underestimate the number of phenotypes in a population? Is this question unique because they say at least 1?

Edit: I get that you have two crosses and each is independent so it's a 50% probability of having a color blind girl each time, but I still don't get how they reached 75%

You can answer this question in three ways.

Option 1) By process of elimination (my favorite). You know that the chance of one girl to be color blind is 50%, so you must also know that the probability must increase when you have two girls and the question is asking for "at least one" to be color blind. This alone should hint you that A and B are incorrect. Now you must decide if it's C and D. The only way D can be correct if the trait is dominant, but since it's recessive the answer must be C.

Option 2) You can approach it by figuring out the probability of having both girls with normal vision, and then subtracting that from 100% to give you the probability of having at least one of them color blind. The chance of having two normal girls is 50% x 50% = 25%. 100% - 25% = 75%.

Option 3) This is the long, orthodox method to solve this question. The question is asking about the chance of having "at least one" of the girls color blind. There are 3 scenarios for this:

1. Girl 1 is color blind and Girl 2 is normal. (25%)
2. Girl 1 is normal and girl 2 is color blind. (25%)
3. Both girls are color blind. (25%)

Adding all these percentages should give you answer C.

 

[slz1900]

Thanks. I think I got confused because it didn't immediately occur to me that each daughter was independent and had a 50% chance. POE was the way to go 👍.

 

[Postictal Raiden]

Thanks. I think I got confused because it didn't immediately occur to me that each daughter was independent and had a 50% chance. POE was the way to go 👍.

I got it wrong right off the bat too, but when I began to work out the problem, I realized where I made my mistake.

 

[Clinicall]

So I'm confused. If the answer had asked "If the parents have a girl, what is the probability of her being colorblind" would it then be 50%? Is it because they ask "what is the probability of ATLEAST ONE of the girls is colorblind"? that gives us the answer of 75%?

 

[Postictal Raiden]

So I'm confused. If the answer had asked "If the parents have a girl, what is the probability of her being colorblind" would it then be 50%? Is it because they ask "what is the probability of ATLEAST ONE of the girls is colorblind"? that gives us the answer of 75%?

Yes

The chance that one of two girl to be color blind is 50%. The chance of both girls having the disease is 25% (50%x50%). Add both probabilities together and you get 75%.

There are other, easier, ways to solve this particular problem. Read the previous posts.

 

[image187]

So I'm confused. If the answer had asked "If the parents have a girl, what is the probability of her being colorblind" would it then be 50%? Is it because they ask "what is the probability of ATLEAST ONE of the girls is colorblind"? that gives us the answer of 75%?

Yeah, you're right. This question isn't really about genetics though, it's more about statistics. Think about it this way: If you flip a coin you have a 50% chance of getting heads. Now, if you flip a coin 20 times, what is the chance that at least 3 times will be heads. This question is more difficult to solve than the one above, but you get the point (it's actually solved with a very easy statistical formula). The answer is obviously not 50%, it's much much more because each additional flip of the coin increases the total chance of getting atleast 3 heads.

 

[DEFINATELY]

Are you using the ExamKrackers books? If yes, is the 7th Edition copyrighted in 2007?
Thanks