In a manufacturing process where 8% of all items are defective, an inspector at the end of the production line selects some items for inspection. Suppose that 64% of the defective items and 16% of the good items go through the inspection. Find the probability that an item

a. has an inspection
b. is defective given that it has an inspection.

(a) The probability that an item  has an inspection is 0.1984.

(b) The probability that an item is defective given that it has an inspection is 0.2581.

Step-by-step explanation:

The law of total probability states that, if B₁, B₂, B₃,... are part of a sample space S, then for any event A,

The condition probability of an event A given that another event B has already occurred is:

Denote the events as follows:

X = an item is defective

Y = the item is being inspected by the inspector.

The information provided is:

(a)

Compute the probability that an item  has an inspection as follows:

Use the law of total probability:

Thus, the probability that an item  has an inspection is 0.1984.

(b)

Compute the probability that an item is defective given that it has an inspection as follows:

Use the condition probability:

Thus, the probability that an item is defective given that it has an inspection is 0.2581.

easy its decreasing

step-by-step explanation:

because its top point is at the to of the graph on the left side (atleast from the veiw i see it) now if that top point wast in the lower part of the graph it would be increasing hope this have a nice day

a

step-by-step explanation:

the denominator cannot be the same as one of the factors.

8 denominator times 2 denominator = 16

and 7 numerator time 11 = 77

77/16= 77/16 ( they cannot be further simplified)