Refer to Exercise 15. Let E1 be the event that the wafer comes from Lot A, and let E2 be the event that the wafer is conforming. Are E1 and E2 independent? Explain.

Step1 of 3:

A population of 600 semiconductor wafers contains wafers from three lots. Wafers are categorized by lot or they conform to a thickness specification. The number of wafers from each category is given in the table.

Lot |
Conforming |
Non- conforming |
Total |

A |
88 |
12 |
100 |

B |
165 |
65 |
200 |

C |
260 |
40 |
300 |

Total |
513 |
87 |
600 |

It E1 be the event that wafer comes from lot A, and E2 be the event that wafer is conforming.

We have to check whether the events E1 and E2 are independent.

Step 2 of 2 :

Here the events are defined as

E1 ={ wafer comes from lot A}

E2 = { wafer is conforming}

From the table

The total number of wafers that comes from lot A = 100

The total number of wafers that comes from all lots = 600

The total number of wafers that are conformed = 513

So

P(E1) = P(that wafers comes from lot A)

=

=

=

P(E1) = 0.1666

So the probability that wafers comes from lot A = 0.1666.

Similarly

P(E2) = P(that wafers are confirmed)

=

= 513/600

= 0.855

So the probability that wafers are conform to thickness specification = 0.855.