Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Round to
1 answer:
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Answer:
A. a) 24
A. b) 4
B. a) 40320
B. b) 576
Step-by-step explanation:
General formula for Permutations:
A. Concert seats: 2 couple --- total of 4 persons.
a) without restrictions
Since there are no restrictions, but that the order is important (John, Mary, Paul, Michelle isn't the same as Michelle, Mary, Paul, John), it's a permutation calculation.
Then we calculate the permutations of 4, out of 4, so...
24 different ways for them to sit.
b) couples together
Now, we can see the problem as having 2 levels of permutations, first the couples, then inside the couples.
There are 2 ways for the first level or order... couples AB or BA, so 2 possibilities.
Inside each couple, man then woman (MW) or woman then man (WM), so 2 possibilities there too on 2nd level.
Overall 2 * 2 = 4 ways to sit by couple.
B) Single file
a) without restrictions
Again, order is important, so another permutation, not a combination. And since we have no restriction, it can be any sequence.
We then have to calculate the number of permutations of 8 out of 8...
There are 40,320 ways these 8 kids can pass the door.
b) girls first.
So, the four girls have to enter first.... and these four girls can be in any order.. how many permutations? P(4,4)... so 24 as calculated above.
For the four boys, how many permutations? Yes, again P(4,4)... so 24 again.
Overall, we need to multiply the two... 24 x 24 = 576 ways if the girls enter first, followed by the boys.
Answer:
30% probability that the ball taken from B is red.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
Red ball from urn A:
3/6 = 1/2 probability of getting a red ball from urn A.
Then urn B will have 5 balls, 2 of which are red, so 2/5 probability of getting a red ball.
Blue ball from urn A:
3/6 = 1/2 probability of getting a blue ball from urn A.
Then urn B will have 5 balls, 1 of which is red, so 1/5 probability of getting a red ball.
Total:
3/10 = 0.3 = 30%.
30% probability that the ball taken from B is red.