What is the difference between independent and conditional probability? Which one requires the use of the Addition Rule?Explain.
2 answers:
Answer:
In probability, independent events are those that if one event occurs, it does not change the probability of the other event.
Whereas conditional probability is defined as the probability of one event occurring with some relationship to one or more other events.
The addition rule is used for both the independent and conditional probabilities.
For independent event the probability is shown as :
For conditional:
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Answer:
16.2 m
Step-by-step explanation:
First, we can draw a picture. The cable goes from the top of the pole to the ground (with the pole on the right in my drawing), and the point on the ground is 10 m away from the base of the pole. This forms a right triangle, with the right angle being between the 10 m distance and the pole itself. We can then apply the Pythagorean Theorem, so
a²+b²=c², with c being the side opposite the right angle (the cable), getting us
10²+(length of pole)² = 19²
19²-10²=(length of pole)²
= 261
square root both sides to isolate the length of the pole
length of pole ≈ 16.2 m
Answer: The table is shown in the attached image
- Row One: 19, 28, 47
- Row Two: 19, 33, 52
- Row Three: 38, 61, 99
The commas are not to be entered in any of the boxes. Just the numbers only.
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Explanation:
"47 seventh graders were surveyed" means that 47 goes in the last value of the first row. This is the total of the 7th graders. Of this total, 19 pack their lunches (ie bring them from home). That indicates 47-19 = 28 seventh graders buy their lunch.
For row one, we have the values: 19, 28, 47 in that exact order when going from left to right.
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We use the same idea for the 8th graders.
52 total eighth graders, 33 buy their lunch
52-33 = 19 pack their lunch
For row two, the values from left to right are: 19, 33, 52 in that exact order.
To get the values in row 3, we add up everything that's over top of it.
Meaning for column 1, we have 19+19 = 38 total students who pack their lunch. In column 2, there are 28+33 = 61 people who buy their lunch. Lastly, column 3 we have 47+52 = 99 students overall.
For row three, the values from left to right are: 38, 61, 99
Note that adding the first two items of row three gets us 38+61 = 99
It's not a coincidence that this is happening. This is just another way to get the grand total of 99. You could also add up the four values that are not in the total column or total row to get 19+28+19+33 = 99. Again, this is not a coincidence we end up with 99.
Refer to the table below to see a summary.
