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.
0.004 (type an integer or a decimal.)

another couple plans to have two children. determine the probability that both children will be born with the condition.
0.00012 (type an integer or a decimal.)

determine the probability that the first will be born with the condition and the second will not.
0.00388 (type an integer or a decimal.)

determine the probability that the first will not be born with the condition and the second will.
0.003984 (type an integer or a decimal.)

determine the probability that neither will be born with the condition.
(type an integer or a decimal.)

Explanation:

Define the events and probabilities

Using the Conditional Probability and Dependent Events knowledge points

$$
LATEXBLOCK0
$$

Determine independence of the events

Using the Independent Events and Dependent Events knowledge points

$$
LATEXBLOCK1
$$

Calculate probability for one child

Using the Probability Scale knowledge point

$$ P(\text{one child with condition}) = 0.004 $$

Calculate probability for both children

Using the Multiplication Rule for Independent Events and Dependent Events knowledge points

$$ P(C_1 \cap C_2) = P(C_1) \times P(C_2 \mid C_1) = 0.004 \times 0.03 = 0.00012 $$

Calculate remaining joint probabilities

Using the Complementary Events and Conditional Probability knowledge points

$$
LATEXBLOCK2
$$

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>.

Question 3

The probability that both children will be born with the condition is <blank>0.00012</blank>.

Question 4

The probability that the first will be born with the condition and the second will not is <blank>0.00388</blank>.

Question 5

The probability that the first will not be born with the condition and the second will is <blank>0.003984</blank>.

Question 6

The probability that neither will be born with the condition is <blank>0.992016</blank>.