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1 answer:
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a) 1/6
b) 1/36
c)
1H, 2H, 3H, 4H, 5H, 6H
1T, 2T, 3T, 4T, 5T, 6T
Step-by-step explanation:
a)
The probability of a certain event A to occur is given by
where
a is the number of successfull outcomes, in which event A occurs
n is the total number of possible outcomes
In this problem, the event is
"getting a 6 when throwing a dice once"
We know that the possible outcomes of a dice are six: 1, 2, 3, 4, 5, 6, so we he have
The successfull outcome in this case is only if we get a 6, so only 1 outcome, therefore
So, the probability of this event is
b)
In this case instead, we are throwing the dice twice.
The two throws of the dice are independent events (one does not depend on the other): the probability that two independent events A and B occur at the same time is given by the product of the individual probabilities,
where
is the probability that event A occurs
is the probability that event B occurs
Here we have:
- Event A is "getting a 6 in the first throw of the dice". We already calculated this probability in part a), and it is
- Event B is "getting a 6 in the second throw of the dice". Since the dice has not changed, the probability is still the same, so
Therefore, the probability of getting a 6 on both throws is:
c)
In this problem, we have:
- A dice that is thrown once
- A coin that is also thrown once
The dice has 6 possible outcomes, as we stated in part a):
1, 2, 3, 4, 5, 6
While the coin has two possible outcomes:
H = head
T = tail
So, in order to find all the outcomes of the two events combined, we have to combine all the outcomes of the dice with all the outcomes of the coin.
Doing so, using the following notation:
1H (getting 1 with the dice, and head with the coin)
The possible outcomes are:
1H, 2H, 3H, 4H, 5H, 6H
1T, 2T, 3T, 4T, 5T, 6T
So, we have a total of 12 possible outcomes.
Answer:
a.
The 95% confidence interval for the proportion of all American adults who have a gun in their home is (0.4066, 0.4734). This means that we are 95% sure that the true population proportions of American adults who have a gun in their home is between these two values.
b.
The confidence level is the probability of the confidence interval containing the population proportion.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
Poll of 850 randomly selected American adults and finds that 44% of those surveyed have a gun in their home.
This means that
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval for the proportion of all American adults who have a gun in their home is (0.4066, 0.4734). This means that we are 95% sure that the true population proportions of American adults who have a gun in their home is between these two values.
b. Explain what is meant by 95% confidence in this context.
The confidence level is the probability of the confidence interval containing the population proportion.