1. A human gene carries a certain disease from a mother to her child with a probability rate of 0.58. That is, there is a 58% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has five children. Assume that the infections, or lack thereof, are independent of one another. Find the probability that all five of the children get the disease from their mother.
A) 0.934
B) 0.066
C) 0.013
D) 0.018
I don't know how to set this problem up to get the answer...
2. Which of the following represents the P(AC)?
(i) The probability that event A does not occur
(ii) 1 - P(AC)
(iii) 1 minus the probability that event A does occur
(iv) 1 - P(A)
A) i, iii, and iv
B) ii
C) i and iii (I chose this one)
D) iii and iv
E) i, ii, iv
3. What is the probability of an event?
A) A collection of outcomes
B) A number between 0 and 1 that reports the likelihood of the event's occurrence
C) A single attempt or realization of a random phenomenon
D) Its long-run relative frequency
E) Two of the above (I chose this one?)
1. To find the probability that all five children get the disease from their mother, we can multiply the individual probabilities for each child getting infected since the infections are assumed to be independent.
Given that the probability rate of passing on the disease from the mother to the child is 0.58 (or 58%), the probability of a child getting infected is 0.58.
To find the probability that all five children get infected, we raise this probability to the power of 5 (since there are five children). So the probability that all five children get the disease is:
0.58^5 = 0.013
Therefore, the correct answer is C) 0.013.
2. The correct answer is B) ii.
P(AC) represents the probability of event A not occurring. The complement rule states that the probability of an event A not occurring is equal to 1 minus the probability of A occurring. So, 1 - P(AC) would represent the probability of event A occurring.
3. The correct answer is B) A number between 0 and 1 that reports the likelihood of the event's occurrence.
The probability of an event is a number between 0 and 1 that represents the likelihood of the event occurring. It can be thought of as the relative frequency of the event occurring in the long run. Outcomes and attempts of a random phenomenon are related to probability, but they do not directly define what probability is. Therefore, the correct option is B) A number between 0 and 1 that reports the likelihood of the event's occurrence.
1. To find the probability that all five children get the disease from their mother, we can multiply the probability of each child getting the disease.
The probability of each child getting the disease is 0.58 (58%), as given in the problem.
Since the infections are independent of one another, we can multiply the probabilities together:
P(all five children get the disease) = 0.58 * 0.58 * 0.58 * 0.58 * 0.58
Calculating this expression gives us approximately 0.018.
Therefore, the answer is D) 0.018.
2. P(AC) represents the probability that event A does not occur.
So, the answer is A) i, iii, and iv.
3. The probability of an event is B) A number between 0 and 1 that reports the likelihood of the event's occurrence.