Question

The data from 200 machine parts are summarized as follows:
Depth of Bore
Edge Condition above target below target
Coarse 15 10
Moderate 25 20
smooth 50 80
a) What is the probability that a part selected has a moderate edge condition and a below-target bore depth?
b) What is the probability that a part selected has a moderate edge condition or a below target bore depth?
c) What is the probability that a part selected does not have a moderate edge condition

Answer 1

Let's denote some events:
\(C\): coarse edge
\(M\): moderate edge
\(S\): smooth edge

\(A\): above target
\(B\): below target

a) Find \(P(M\cap B)\). This is given by the ratio of the number of machine parts that have both qualities (25) to the total (200), or \(\dfrac{25}{200}=\dfrac{1}{8}\).

b) Find \(P(M\cup B)\). The probability of a union of events is given by the following formula:
\[P(M\cup B)=P(M)+P(B)-P(M\cap B)\]
As before, each probability is a ratio of the parts that satisfy a given characteristic to the total number of parts.

c) Find \(P(\overline{M})\), or \(P(M^C)\), where \(\overline{M}\) and \(M^C\) denote the same thing: the complement of \(M\), i.e. the event that \(M\) does not occur.
\[P(\overline{M})=1-P(M)\]

Answer 2

in part a) the intersection of M with B should be 20 not 25 am i right @SithsAndGiggles

Answer 3

b) -- P(M)=45/200
P(B)=110/200
and P(MUB)=27/40

Answer 4

@yama_aryayee, correct, I misread my own table :)