Before a plank of wood is accepted by a lumber yard, a special machine is used to measure the thickness of the wood for specification compliance.
Tests are performed at each 0.1-feet point of the plank. The entire 0.1-foot section is
accepted if the measured thickness meets the minimum value of 2-inch; otherwise the
entire section is rejected.
Suppose from past experience that 90% of all planks manufactured were
found to be in compliance with specifications. However, the machine measuring tests results
determination are only 80% reliable; that is, there is a 20% chance that a conclusion based
by the machine is incorrect.
Let A be the event that the actual thickness of a plank is at least 2-in
Let B be the event that the measured thickness is greater than 2-in

(a) What is the probability that a particular plank is well manufactured (at least
2-in thick) and will be accepted by the Highway Department, i.e., P[ A and B ]?

(b) What is the probability that a plank is poorly manufactured (thickness less than 2-in) but will
be accepted on the basis of the machine test measuring results, i.e., P[ A′ and B ]?

(c) What is the probability that if a plank is well manufactured, it will be accepted on the basis of
the machine result tests, i.e., P[ B | A ]?


Thank you so much!

Ooh Im doing probability right now haha

Formula for conditional probability is P(A|B) = P(A ^ / P(B)
It means Probability of A given B = Probably of A and B at same time divided by Probability of B

Edit damn smileys

First 2 are just P(A)x P(B)

This post was edited by Branket on May 21 2014 07:44am

(a)

P(A and B.) = 90% * 80% = 72%

that is, assuming that the reliability of the measurement process is independant from the thickness of the plank :
80% of the planks with thickness > 2-in will be measured as > 2-in,
as well as :
80% of the planks with thickness < 2-in will be measured as < 2-in.

(b)

P(A' and B.) = 10% * 20% = 2%

for 10% of the planks, thickness < 2-in, and among them, 20% are still accepted by the machine, following an incorrect measurement.

(c)

P( B | A ) = 80%

this is a straight answer from the text : for a plank with thickness > 2-in, the test is correct 80% of the time, and that means in this case that the plank is accepted.

This post was edited by feanur on May 21 2014 07:44am

Oo good luck