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4 The following table gives the league and division of each of the twenty World Series Baseball winners. The following events are defined. A: American League B; Cen...

Question

4 The following table gives the league and division of each of the twenty World Series Baseball winners. The following events are defined. A: American League B; Central Division League National American Then find the following: Eastern a. P(A n B): Division Central Western b. P(A U B)P(AIB)d. Given that the team wins in the National league, then find the probability that it is from Western Division.

4 The following table gives the league and division of each of the twenty World Series Baseball winners. The following events are defined. A: American League B; Central Division League National American Then find the following: Eastern a. P(A n B): Division Central Western b. P(A U B) P(AIB) d. Given that the team wins in the National league, then find the probability that it is from Western Division.



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In the baseball World Series, two teams play games until one team or the other wins four times. Suppose team A should win each game with probability 0.6. The probabilities for team A's record (given as wins/losses) in the World Series are shown. Find the probability of each event indicated below. $$\begin{array}{|l|l|l|l|l|} \hline \text { Wins/losses } & 0 / 4 & 1 / 4 & 2 / 4 & 3 / 4 \\ \hline \text { Probability } & 0.0256 & 0.0615 & 0.0922 & 0.1106 \\ \hline \end{array}$$ $$\begin{array}{|l|l|l|l|l|} \hline \text { Winshosses } & 4 / 3 & 4 / 2 & 4 / 1 & 4 / 0 \\ \hline \text { Probability } & 0.1659 & 0.2073 & 0.2073 & 0.1296 \\ \hline \end{array}$$ (a) Team A wins the World Serics (b) Team B wins the World Series (c) One team wins all four games (d) The teams play six or seven games

A junior from School A and a senior from School B is going to be 0.25 times 0.2 because this is an end probability, not an or so. We multiply them together and you get P equals 0.5 or 5%.

So when this problem were given to schools and we're told what percentage of those schools air freshman, sophomore, juniors and seniors And we're interested in forming a committee. And this question asks us to find the probability that our committee has two juniors. The thing to note, though, is that this committee is made up of one student from each school, right? So that means since we're getting a student from each school, these two students of selecting our independent of each other, right? So that means we want the probability that we get a junior from the first school and a junior from the second school or schools and be right. But these two events are independent, and that means right, this comma is another way. Sometimes you'll see instead of the word and right, so another way we can write this Using the formula from the book is the probability that we choose a junior from the first school times, the probably that we choose a junior from the second school right? But we can use these used these tables that are given to us to find. This probably is so in the first school school, a 25% of the students are juniors, so we have 25%. We can also write that as 14 multiplied. Well, it's school B. 24% of these students, our juniors. Right. So we can write that as 24 over 100. Okay, we can cross simplify here, divide this by four. We get one, divide this by four, we get six. And so we're left with point go six as our probability that our committee is made up of two juniors.


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