Question

certain congenital conditions are polygenic in nature. typically, the chance that an offspring will be born with a polygenic condition is small. however, once an offspring is born with the condition, the probability that future offspring of the same parents will be born with the same condition increases. assume that the probability of a child being born with condition a is 0.004. if a child is born with this condition, the probability of a future child being born with the same condition becomes 0.03.

are the events of the births of two children in the same family with condition a independent?

yes
no

a couple plans to have one child. determine the probability that the child will be born with this condition.
(type an integer or a decimal.)

Explanation:

Define events and probabilities

Using the Independent Events and Dependent Events knowledge points
Let \(C_1\) be the event that the first child is born with condition A, and \(C_2\) be the event that the second child is born with condition A.

$$
LATEXBLOCK0
$$

Determine independence

Using the Independent Events and Dependent Events knowledge points

$$
LATEXBLOCK1
$$

Determine probability for a single child

The problem states that a couple plans to have one child. The baseline probability of a child being born with condition A is given directly.

$$ P(\text{condition A}) = 0.004 $$

Answer:

Question 1

• Yes
• No (Correct answer)

Question 2

The probability that the child will be born with this condition is <blank>0.004</blank>.