Genetics-Two heterozygous brown-eyed (Bb)

[jena]

Hi,

My Question:

Two heterozygous brown-eyed (Bb) individual have five children.What ist he probability that three will have blue eyes?

Answer:

Would the possibility be zero for all three since blue eyes is recessive

Thank You

 

[jena]

Hi,

I looked over the question again and I know for sure this isn't the right answer. I do know that I should use a binomial expansion, so if the

Probability of blue eyes is 1/4 then I would square this and get

P(blue)=(1/4)^2=.0625*100=6.25%

Is this correct?

Thank You

 

[Moonbear]

Why are you squaring the probability?

This one is also a bit trickier because they aren't just asking the probability of 3 having blue eyes, but 3 out of 5. That will change how you do your calculations somewhat.

 

[amcavoy]

You might try to find the probability of 1/5 of the children having blue eyes. Having 5 kids would do what to that probability?

 

[jena]

The probability of having 1 child having blue eyes is 20% right, so to figure the probability of three children having blue eyes would be

P(blue)=(1/5)^3 or .80 %

Is this correct?

 

[gerben]

The probability of having 1 child having blue eyes is 20% right

No it is not 20%, why do you think that?

 

[amcavoy]

You had it right the first time when you said the probability of one child having blue eyes is 1/4, or 25%. Now try it.

 

[jena]

I thought it was 20% because 1/5 is .20 multiply that by 100 and you get 20%, but I know what I did wrong this time all I have to do is use the binomial equation.

P=((n!)/(x!(n-x)!))*((p^x)(q^(n-x)))

I used the following steps to come up with an answer

Step 1: Calculate the individual probabilities
• P(blue eyes)= p=1/4
• P(brown eyes)=q=3/4

Step 2: Determine the number of events
• n=total number of children=5
• x= number of brown eyed children=3

Step 3: Substitute the values for p, q, x, and n in the binomial expansion equation(like above)

Finally

P=((5!)/(3!(5-3)!))*(((1/4)^3)((3/4)^(5-3)))
P=8.78%

I hope this time around that's right

 

[gerben]

Yes, it is right!