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5. An online bookseller uses one of four shipping companies to send packages to its customers. Any package can be sent with one and only one of these companies. Denote the following events: C1: the package is shipped with company 1 C2: the package is shipped with company 2 C3: the package is shipped with company 3 C4: the package is shipped with company 4 The bookseller uses the shipping companies with the following probabilities: P(C1) = 0.5, P(C2) = 0.25, P(C3) = 0.125, P(C4) = 0.125 Let X be the event that the package arrives on time at its destination. Depending on the shipping company used, the probability of X varies: P(X/C1) = 0.85, P(X/C2) = 0.9, P(X/C3) = 0.8, P(X/C4) = 0.8 5.1) Compute the numerical value of P(C2 U C3). 5.2) Given that a package has arrived on time what is the probability that it was shipped with company C1? 5.3) Are the events C1' and X independent? 5.4) What is the probability that package will not arrive on time exactly 3 times out of 10 times? 

          5. An online bookseller uses one of four shipping companies to send packages to its customers. Any package can be sent with one and only one of these companies. Denote the following events:
C1: the package is shipped with company 1
C2: the package is shipped with company 2
C3: the package is shipped with company 3
C4: the package is shipped with company 4
The bookseller uses the shipping companies with the following probabilities:
P(C1) = 0.5, P(C2) = 0.25, P(C3) = 0.125, P(C4) = 0.125
Let X be the event that the package arrives on time at its destination. Depending on the shipping company used, the probability of X varies:
P(X/C1) = 0.85, P(X/C2) = 0.9, P(X/C3) = 0.8, P(X/C4) = 0.8
5.1) Compute the numerical value of P(C2 U C3).
5.2) Given that a package has arrived on time what is the probability that it was shipped with company C1?
5.3) Are the events C1' and X independent?
5.4) What is the probability that package will not arrive on time exactly 3 times out of 10 times?
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5. An online bookseller uses one of four shipping companies to send packages to its customers. Any package can be sent with one and only one of these companies. Denote the following events: C1: the package is shipped with company 1 C2: the package is shipped with company 2 C3: the package is shipped with company 3 C4: the package is shipped with company 4 The bookseller uses the shipping companies with the following probabilities: P(C1) = 0.5, P(C2) = 0.25, P(C3) = 0.125, P(C4) = 0.125 Let X be the event that the package arrives on time at its destination. Depending on the shipping company used, the probability of X varies: P(X/C1) = 0.85, P(X/C2) = 0.9, P(X/C3) = 0.8, P(X/C4) = 0.8 5.1) Compute the numerical value of P(C2 U C3). 5.2) Given that a package has arrived on time what is the probability that it was shipped with company C1? 5.3) Are the events C1' and X independent? 5.4) What is the probability that package will not arrive on time exactly 3 times out of 10 times?

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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An online bookseller uses one of four shipping companies to send packages to its customers. Any package can be sent with one and only one of these companies. Denote the following events: C1: the package is shipped with company 1, C2: the package is shipped with company 2, C3: the package is shipped with company 3, C4: the package is shipped with company 4. The bookseller uses the shipping companies with the following probabilities: P(C1) = 0.5, P(C2) = 0.25, P(C3) = 0.125, P(C4) = 0.125. Let X be the event that the package arrives on time at its destination. Depending on the shipping company used, the probability of X varies: P(X|C1) = 0.85, P(X|C2) = 0.9, P(X|C3) = 0.8, P(X|C4) = 0.8. 5.1) Compute the numerical value of P(C2 U C3). 5.2) Given that a package has arrived on time, what is the probability that it was shipped with company C1? 5.3) Are the events C1' and X independent? 5.4) What is the probability that the package will not arrive on time exactly 3 times out of 10 times?
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Transcript

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00:01 Here we are given p of h1 equal 0 .5, p of h2 equal to 0 .25, and p of h3 equal 0 .125, and p of h4 is 0 .125, p of x with the condition h1 is given as 0 .85, and p of x by h2 is 0 .9, and p of x by h2 is 0 .9, and p of x by h3 is equal to 0 .8 .5.
00:32 8 comma p of x by h 4 equal to 0 .8.
00:39 The question is we need to find p of h2 union h3 which is equal to p of h2 plus p of h3 minus p of h2 and h3 that is h2 intersection h3 so now to find this one so which is equal to p of h2 plus p of h3 because a h2 and h3 are disjoint so the final value equal to zero so substitute the value is 0 .25 plus 0 .125 which is 0 .375 then come to the second option here we have to use the total probability rule that is p of x equal to p of h1 into p of h1 plus p of h2 into p of xx h2 plus p of h3 into p of x by h3 plus p of h4 into p of x by h4 so which is equal to 0 .5 multiplied by 0 .85 plus 0 .25 multiplied by 0 .9 plus 0 .125 multiplied by 0 .15 multiplied by 0 .8 plus 0 .125 multiplied by 0 .8 and the total is 0 .85.
02:11 Third one.
02:14 Now we can use the base formula to solve this value...
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