A business office orders paper supplies from one of three vendors, V₁, V₂, or V₃. Orders are to be placed on two successive days
, one order per day. Thus, (V₂, V₃) might denote that vendor V₂ gets the order on the first day and vendor V₃ gets the order on the second day.
a. List the sample points in this experiment of ordering paper on two successive days.
b. Assume the vendors are selected at random each day and assign a probability to each sample point.
c. Let A denote the event that the same vendor gets both orders and B the event that V₂ gets at least one order. Find P( A), P( B), P( A ∪ B), and P( A ∩ B) by summing the probabilities of the sample points in these events.
a. List the sample points in this experiment of ordering paper on two successive days.
b. Assume the vendors are selected at random each day and assign a probability to each sample point.
c. Let A denote the event that the same vendor gets both orders and B the event that V₂ gets at least one order. Find P( A), P( B), P( A ∪ B), and P( A ∩ B) by summing the probabilities of the sample points in these events.
1 answer:
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Answer:
Step-by-step explanation:
We can see by some observation that this is not linear because the slopes aren't constant.
So, let's see if it's quadratic. Suppose that it is and the function we want to find is:
Plug in some of the given values into the equation:
3 = a + b + c ------------ eq 1
1 = 9a + 3b + c ------------ eq 2
1.5 = 4a + 2b + c ------------ eq 3
Let's multiply eq 3 by 2 and then subtract it from equation 2:
1 = 9a + 3b + c
- 3 = 8a + 4b + 2c
----------------------------
-2 = a - b - c
Now, add this equation to eq 1:
-2 = a - b - c
+ 3 = a + b + c
-----------------------
1 = 2a
a = 1/2 = 0.5
Now, plug this value of a back into both eq 3 and eq 1:
Eq 3: 1.5 = 4 * 0.5 + 2b + c ⇒ 1.5 = 2 + 2b + c ⇒ -0.5 = 2b + c ----- eq 5
Eq 1: 3 = 0.5 + b + c ⇒ b + c = 2.5 ------ eq 4
So, we have a system of linear equations. Subtract eq 4 from eq 5:
2b + c = -0.5
- b + c = 2.5
-------------------------
b = -3
Substitute this value of b into b + c = 2.5 and solve for c:
-3 + c = 2.5
c = 5.5
So, a = 0.5, b = -3, and c = 5.5. Now, our equation is:
Hope this helps!