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guapka [62]
3 years ago
5

Suppose a birth defect has a recessive form of inheritance. In a study population, the recessive gene (a) initially has a preval

ence of 25%. A subject has the birth defect if both maternal and paternal genes are of type a.
a.In the general population, what is the probability that an individual will have the birth defect, assuming that maternal and paternal genes are inherited independently.

A further study finds that after 10 generations (≈ 200 years) a lot of inbreeding has taken place in the population. Two subpopulations (populations A and B), consisting of 30% and 70% of the general population, respectively, have formed. Within population A, prevalence of the recessive gene is 40%, whereas in population B it is 10%.

b.Suppose that in 25% of marriages both people are from population A, in 65% both are from population B, and in 10% there is one partner from population A and one from population B.

What is the probability of a birth defect in the next generation?

c.Suppose that a baby is born with a birth defect, but the baby’s ancestry is unknown. What is the posterior probability that the baby will have

1. both parents from population A?

2. both parents from population B?

3. mixed ancestry (i.e. one parent from population A and one from population B)?
Mathematics
1 answer:
BabaBlast [244]3 years ago
4 0

Answer:

Step-by-step explanation:

a) Maternal gene = 0.25; Paternal gene = 0.25

Probability having a birth defect = 0.25 X 0.25 = 0.625

b) P(A) = 0.30; P(B) = 0.70

P(A)*P(B) = 0.30 X 0.70 = 0.021

For marriage:

25%: P(A)*P(A)*0.25 = 0.09 X 0.25 = 0.0225

65%: P(B)*P(B)*0.65 = 0.049 X 0.65 = 0.03185

10%: P(A)*0.10 = 0.03 and P(B)*0.10 = 0.07

P(A)*P(B) = 0.03 X 0.07 = 0.0021

Probability of a defect birth in the next generation = 0.0225 + 0.03185 + 0.0021 = 0.05645

c) 1. P(A)*P(A) = 0.09

2. P(B)*P(B) = 0.049

3. P(A)*P(B) = 0.021

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It’s a new semester!students are grouped into three clubs, which each has 10,4 and 5 students.In how many ways can teacher sleep
My name is Ann [436]

The total number of ways to select 2 students from the 3 clubs is 55 ways.

Since there are three clubs which each has 10, 4 and 5 students, and we require the number of ways a teacher can select 2 students so that they are from different clubs.

Since order doesn't matter and anybody can be chosen first, we use combination theory.

<h3 /><h3>Number of ways of selecting from the first two clubs</h3>

Since we have two slots, to select the first person from the first club, we ¹⁰C₁. For the second student from the club of 4, we have ⁴C₁. Also, there are 2 ways of selecting the two students.

So, there are ¹⁰C₁ × ⁴C₁/2!

= 10 × 4/2

= 20 ways from the first two clubs.

<h3 /><h3>Number of ways of selecting from the next two clubs</h3>

For the next two clubs of 4 and 5 students, for the first slot, we have ⁴C₁. For the second student, we have ⁵C₁. Also, there are 2 ways of selecting the two students.

So, there are ⁴C₁ × ⁵C₁/2!

= 4 × 5/2

= 10 ways from the next two clubs.

<h3 /><h3>Number of ways of selecting from the last two clubs</h3>

For the first and last club of 10 and 5 students, for the first slot, we have ¹⁰C₁. For the second student, we have ⁵C₁.  Also, there are 2 ways of selecting the two students.

So, there are ¹⁰P₁ × ⁵P₁/2!

= 10 × 5/2

= 25 ways from the first and last club.

<h3 /><h3>Total number of ways of selecting two students from the 3 clubs.</h3>

So, the total number of ways to select 2 students from the 3 clubs is 20 + 10 + 25 = 55 ways.

So, the total number of ways to select 2 students from the 3 clubs is 55 ways.

Learn more about combinations here:

brainly.com/question/25990169

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