1. Mark charges $10 an hour to babysit with an additional flat fee of $20 for each babysitting job. He wants to purchase a new g
2 answers:
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Answer:
(a) The proportion of women who are tested, get a negative test result is 0.82.
(b) The proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.
Step-by-step explanation:
The Bayes' theorem states that the conditional probability of an event <em>E</em>, of the sample space <em>S,</em> given that another event <em>A</em> has already occurred is:
The law of total probability states that, if events <em>E</em>₁, <em>E</em>₂, <em>E</em>₃... are parts of a sample space then for any event <em>A</em>,
Denote the events as follows:
<em>X</em> = fetus have a chromosome abnormality.
<em>Y</em> = the test is positive
The information provided is:
Using the above the probabilities compute the remaining values as follows:
(a)
Compute the probability of women who are tested negative as follows:
Use the law of total probability:
Thus, the proportion of women who are tested, get a negative test result is 0.82.
(b)
Compute the value of P (X|Y) as follows:
Use the Bayes' theorem:
Thus, the proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.
Answer:
(a) The probability distribution is valid.
(b) The probability that x = 30 is 0.30.
Step-by-step explanation:
The probability distribution of the random variable <em>X</em> is:
<em> x</em>: 20 | 25 | 30 | 35
f (<em>x</em>): 0.20 | 0.15 | 0.30 | 0.35
(a)
The properties of a probability distribution are:
- 0 ≤ P (X) ≤ 1
- ∑ P (X) = 1
All the probability value are more than 0 and less than 1.
Compute the sum of all the probabilities as follows:
The sum of all probabilities is 1.
Thus, the probability distribution is valid.
(b)
Consider the probability distribution table.
The probability of <em>X</em> = 30 is,
P (X = 30) = 0.30.
Thus, the probability that x = 30 is 0.30.