A data scientist studying a manufacturing process classifies each item produced by the process as either Poor, Acceptable, or Excellent. Assume that the classes of different items are independent of each other and that each item falls into the classes according to the following probabilities: Poor Acceptable Excellent
0.25 0.6 0.15

The data scientist receives three items produced by the manufacturing process.
Find the chance that:
a. all of items are Acceptable
b. none of the items is Acceptable
c. at least one of the items is Excellent
d. not all of the items are Excellent
e. there is one item of each class

0.214 ; 0.064 ; 0.3859 ; 0.9966 ; 0.135

Step-by-step explanation:

Given the distribution :

Poor ___ Acceptable Excellent

0.25 0.6 0.15

The data scientist receives three items produced by the manufacturing process.

Find the chance that:

a. all of items are Acceptable

0.6 * 0.6 * 0.6 = 0.6^3 = 0.214

b. none of the items is Acceptable

P(not acceptable) = 1 - p(acceptable) = 1 - 0.6 = 0.4

0.4 * 0.4 * 0.4 = 0.4^3 = 0.064

c. at least one of the items is Excellent

P(atleast one) = 1 - P(none)

P(not excellent) = 1 - 0.15 = 0.85

P(none is excellent) = 0.85^3 = 0.614125

Hence,

P(atleast one is excellent) = 1 - 0.614125 = 0.3859

d. not all of the items are Excellent

P(not all) = 1 - p(All)

P(all excellent) = 0.15^3 = 0.003375

P(not all are excellent) = 1 - 0.003375 = 0.9966

e. there is one item of each class:

P(poor) * p(acceptable) * p(excellent) * (number of classes)!

0.25 * 0.6 * 0.15 * 3!

= 0.135

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.