T is the first one bc it is just look it up
Answer:
Step-by-step explanation:
a) Two events A,B are said to be mutually exlusive if any of the following occurs.
- A and B have an empty intersection
- A= B^c and their union is the whole sample space
- P(A intersection B) =0
REcall the following formula

Note that P(A) + P(B) = 1.1. Since the probability is always a number between 0 and 1, it must happen that
, otherwise,
would have a probability greater than 1. Hence, A, B are not mutually exclusive.
b) by definition, if two events are indepent, we have that the probability of the intersection is equal to products of their probabilites. Or

c) Recall that if we have mutuallly exclusive events A, B, then we have that
, if they were independent, we would have the following

which necesarilly implies that at least one of the two events has 0 probability. (THis is not the case)
Answer:
We can assume that the statistic is 

So the p value obtained was a very high value and using the significance level given
we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5
Step-by-step explanation:
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 3/5 or not.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion
is significantly different from a hypothesized value
.
Calculate the statistic
We can assume that the statistic is 
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided
. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:

So the p value obtained was a very high value and using the significance level given
we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5
Duck iimwisis is the time is the last day to a week or two or three days of February and February