Probability and also Statistics for Engineering and also Science, nine Edition

Authors: Jay L. Devore

ISBN-13: 978-1305251809

See our solution for Concern 17E from Chapter 2 from Devore's Probcapability and Statistics for Engineering and also Science.

You are watching: Let a denote the event that the next request for assistance

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Let

*A*signify the occasion that the following request for assistance from a statistical software application consultant relates to the SPSS package, and let

*B*be the occasion that the following research is for aid via SAS. Suppose that P(A) =. 30 and also P(B) = .50...

Tip 1 of 2

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**Step 1**Let A be the occasion that the next request for assistance is regarded SPSS package.Let B be the event that the next repursuit for assistance is pertained to SAS package. Given probabilities of the events. <eginarraylPleft( A ight) = 0.30\Pleft( B ight) = 0.50endarray>

**Tip 2: (a)**The sum of probabilities of occasions A and also B is not 1. The factor being that the events A and also B are not disjoint. Meaning, apart from given 2 software packages (SPSS and also SAS), tright here could be other packperiods as well. Hence universal collection has some other events acomponent from A and B.

**Tip 3: (b) Compliment of event A**The probcapability of compliment of occasion A is gievn by: <eginarraylPleft( A" ight) = 1 - Pleft( A ight)\ = 1 - 0.3\ = 0.7endarray> Because of this,

**Tip 4: (c) Union of occasion A and B**Because the occasions are disjoint, the probcapacity of interarea of events A and also B is zero. Probcapacity union of events A and also B is: <eginarraylPleft( A cup B ight) = Pleft( A ight) + Pleft( B ight) - Pleft( A cap B ight)\ = 0.3 + 0.5 - 0\ = 0.8endarray>As such,

**Step 4: (d) Intersection of compliments of A and B**making use of De Morgan"s Law <eginarraylPleft( A" cap B" ight) = Pleft< left( A cup B ight)" ight>\ = 1 - Pleft( A cup B ight)\ = 1 - 0.8\ = 0.2endarray>As such,