Answer:
Step-by-step explanation:
4b+8=40
4b=32
b=8
Answer:
E. none of the above
Step-by-step explanation:
20 doesnt fit any of these answers
Solution
Let 0 be the event that the batch has 0 defectives, 1 be the event the batch has 1 defective, and 2 be
the event the batch has 2 defectives. Let 0 be the event that neither selected component is defective.
(0
) = 0.5,(1
) = 0.3, (2
) = 0.2
The event 0 can happen in three different ways: (i) Our batch of 10 is perfect, and we get no defectives in
our sample of two; (ii) Our batch of 10 has 1 defective, but our sample of two misses them; (iii) Our batch
has 2 defective, but our sample misses them.
For (i), the probability is (0.5)(1).
For (ii), the probability that our batch has 1 defective is 0.3. Given that it has 1 defective, the probability
that our sample misses it is (
9
2
)
(
10
2
)
, which is 8
10
. So the probability of (ii) is (0.3) (
8
10).
For (iii), the probability our batch has 2 defective is 0.2. Given that it has 2 defective, the probability that
our sample misses both is (
8
2
)
(
10
2
)
, which is 56
90
. So the probability of (iii) is (0.2) (
56
90). We have therefore found
that
(0
) = (0.5)(1) + (0.3) (
8
10) + (0.2) (
56
90).
We use the general conditional probability formula:
(0
|0
) =
(0 ∩ 0
)
(0
)
=
(0.5)(1)
(0.5)(1) + (0.3) (
8
10) + (0.2) (
56
90)
= 0.5784.
(1
|0
) =
(1∩0
)
(0
)
=
(0.3)(
8
10)
(0.5)(1)+(0.3)(
8
10)+(0.2)(
56
90)
= 0.2776.
(2
|0
) =
(2∩0
)
(0
)
=
(0.2)(
56
90)
(0.5)(1)+(0.3)(
8
10)+(0.2)(
56
90)
= 0.1440.
Answer: 0.5784; 0.2776; 0.1440.
The process works well for a cylinder. It will not work for any other 3-D figures.
_____
I haven't needed to use a method, so there is no comparison.
If you are asked to find the area and volume, then the area/volume ratio, usually you will do it in that order. The "shortcut" is only useful if you don't need either volume or surface area as part of the answer to the question.
