Question

Probability of getting 3 in a single toss of die =

aw of addition: page 168

1. In a manufacturing line there are several operations to produce a component. The probability of getting a surface finish defect on operation-10 is 2/3and probability of getting a dimensional defect on operation-20 is 5/9.After manufacturing finished components,

1. what is the probability of getting a surface finish defect?

2. what is the probability of NOTgetting at least one surface finish defect?

Probability of an event A is P(A) and its complement is Ā. P(A)+P(Ā)=1  or P(Ā) = 1 - P(A)

3. what is the probability of getting both type of defects in the finished component?

If A and B are independent events, the probability that both A and Bwill occur is

P(AB) = P(A∩B) = P(A) x P(B)

4. probability of either surface finish defect ordimensional defect in the finished product is

P(A U B) = P(A) + P(B) – P(A∩B) =

Law of multiplication:

2. In one shift, the probability of tool change on operation 10, P(A) is 0.6. The probability of tool change on operation 20, P(B) is 0.5. The probability of tool change on both operations 10 and 20, P(A∩B) is 0.3.

Note: The tool change on operations are independent.

P(A) = 0.6, P(B) = 0.5 and P(A∩B) = 0.3

Independent:P(AB) = P(A∩B) = P(A) x P(B)

The probability of tool change on both operations 10 and 20

P(A∩B)  = P(A) x P(B) =

The probability of tool change on eitheroperation 10 or 20

P(A) or  P(B) = P(A U B) =

3. The probability of three independent machines on an assembly line with failures are as follows:

P(A failing) = 0.15, P(B failing) = 0.05, P(C failing) = 0.10

1. What is the probability of all three machine work?

Independent failures:

P(A failing) = 0.15,  P(A NOT failing) =

P(B failing) = 0.05, P(B NOT failing) =

P(C failing) = 0.10, P(C NOT failing) =

Probability of all three machines work =

2. What is the probability of the assembly line fail (NOT work)?

Answer 1

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