Write the quotient with the decimal point placed correctly 80 ÷ 50 = 16
2 answers:
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Answer:
The probability of event <em>A</em> is .
The probability of event <em>B</em> is .
Step-by-step explanation:
The sample space of rolling a fair six-sided dice is as follows:
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Now consider the experiment of the computing the sum of the two rolls as follows:
X = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
Number of total outcomes, <em>N</em> = 11.
The probability of an event <em>E</em> is the ratio of the number of favorable outcomes to the total number of outcomes.
The event <em>A</em> is defined as the sum is greater than 5.
The sample space of <em>A</em> is:
A = {6, 7, 8, 9, 10, 11, 12}
n (A) = 7
Compute the probability of event <em>A</em> as follows:
Thus, the probability of event <em>A</em> is .
The event <em>B</em> is defined as the sum is an even number.
The sample space of <em>B</em> is:
B = {2, 4, 6, 8, 10, 12}
n (B) = 6
Compute the probability of event <em>B</em> as follows:
Thus, the probability of event <em>B</em> is .
Answer:
a. n=4148
b. n=3909
c. The sample size is smaller if a known proportion from prior study is used. The difference in sample sizes is 239
Step-by-step explanation:
a. For sample where no preliminary estimate is given, the minimum sample size is calculated using the formula:
Where:
Margin of error
is the assumed proportion
#Let p=0.5, substitute in the formula to solve for n:
Hence, the minimum sample size is 4148
b. If given a preliminary estimate p=0.38, we use the same formula but substitute p with the given value:
Hence, the minimum sample size is 3909
c. Comparing the sample sizes from a and b:
Hence, the actual sample size is smaller for a known proportion from prior a prior study.