Answer:
(a) The probability that an item selected for inspection is classified as defective is 0.01189.
(b) The probability that an item selected at random is classified as non-defective when in fact it is good is 0.99992.
Step-by-step explanation:
Let's denote the events as follows:
G = an item is good
B = an item is bad
D = an item is classified as defective.
<u>Given:</u>
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The probability of producing good items is:
(a)
The law of total probability states that:
Using the law of total probability determine the probability that an item selected for inspection is classified as defective as follows:
Thus, the probability that an item selected for inspection is classified as defective is 0.01189.
(b)
Compute the probability that an item selected at random is classified as non-defective when in fact it is good as follows:
![P(G|D^{c})=\frac{P(D^{c}|G)P(G)}{P(D^{c})} \\=\frac{[1-P(D|G)]P(G)}{1-P(D)} \\=\frac{[1-0.005]\times0.993}{1-0.01189} \\=0.99992](https://tex.z-dn.net/?f=P%28G%7CD%5E%7Bc%7D%29%3D%5Cfrac%7BP%28D%5E%7Bc%7D%7CG%29P%28G%29%7D%7BP%28D%5E%7Bc%7D%29%7D%20%5C%5C%3D%5Cfrac%7B%5B1-P%28D%7CG%29%5DP%28G%29%7D%7B1-P%28D%29%7D%20%5C%5C%3D%5Cfrac%7B%5B1-0.005%5D%5Ctimes0.993%7D%7B1-0.01189%7D%20%5C%5C%3D0.99992)
Thus, the probability that an item selected at random is classified as non-defective when in fact it is good is 0.99992.
Answer:
A
Step-by-step explanation:
- During round 1, Tyler’s group picked 4 purple blocks and 12 blocks of other colors.
Answer:
5940
Step-by-step explanation:
495 x 12 = 5940
Answer:
0.666
Step-by-step explanation:
0.40/0.60 = 0.666
Answer:
Ben's mistake was that he multiplied the area of the original triangle by the scale factor
Step-by-step explanation:
<u><em>The complete question is</em></u>
Beth enlarged the triangle below by a scale of 5. A triangle with a base of 4 centimeters and height of 3.5 centimeters. She found the area of the enlarged triangle. Her work is shown below.
1/2(4)(3.5)(5)= 35 cm2
What was Beth’s error?
we know that
The dilation is a non-rigid transformation that produce similar figures
so
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x ----> the area of the enlarged triangle
y ----> the area of the original triangle
so
The area of the enlarged triangle is equal to the area of the original triangle multiplied by the scale factor squared
therefore
Ben's mistake was that he multiplied the area of the original triangle by the scale factor
