document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186983>Question 1186983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5) Consider the chance experiment in which both tennis racket head size and grip size are noted for a randomly selected customer in a particular store.  The six possible outcomes and their probabilities are given in the table.  <BR>\n" );
document.write( "a) Let event A = grip size of  in.  <BR>\n" );
document.write( "    Find P(A).\r<BR>\n" );
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document.write( "    Interpret this probability.\r<BR>\n" );
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document.write( "b) Find P(AC),\r<BR>\n" );
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document.write( "c) What is the probability that the racket purchased has an oversize head (event B)?\r<BR>\n" );
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document.write( "d) What is the probability that grip size is at least  in.?\r<BR>\n" );
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document.write( "e) What is the probability that the grip size is inch and the head is oversized?\r<BR>\n" );
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document.write( "f) What is the probability that the grip size is inch or the head is oversized?\r<BR>\n" );
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document.write( "g) If the racket has a midsized head, what is the probability that the grip size is inch?\r<BR>\n" );
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document.write( "h) Are the events the grip size of inch and oversized head independent?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849321 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this probability problem.  I'll need the table of outcomes and probabilities to give you specific numerical answers.  However, I will show you the general method.  *Please provide the table so I can complete the calculations.*\r<BR>\n" );
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document.write( "**General Method and Explanation:**\r<BR>\n" );
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document.write( "Let's represent the different head sizes as M (midsized), O (oversized), and E (extra-oversized), and the grip sizes as S (small), M (medium), and L (large).  The table would look something like this (but with actual probabilities):\r<BR>\n" );
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document.write( "| Outcome (Head, Grip) | Probability |<BR>\n" );
document.write( "|---|---|<BR>\n" );
document.write( "| (M, S) | P(M, S) |<BR>\n" );
document.write( "| (M, M) | P(M, M) |<BR>\n" );
document.write( "| (M, L) | P(M, L) |<BR>\n" );
document.write( "| (O, S) | P(O, S) |<BR>\n" );
document.write( "| (O, M) | P(O, M) |<BR>\n" );
document.write( "| (O, L) | P(O, L) |<BR>\n" );
document.write( "| (E, S) | P(E,S) |<BR>\n" );
document.write( "| (E,M) | P(E,M) |<BR>\n" );
document.write( "| (E,L) | P(E,L) |\r<BR>\n" );
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document.write( "*Remember: The sum of all probabilities must equal 1.*\r<BR>\n" );
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document.write( "**a) P(A): Grip size of 1/4 inch**\r<BR>\n" );
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document.write( "Event A corresponds to all outcomes where the grip size is 1/4 inch (which I'm assuming is represented by \"S\" for small in my example).\r<BR>\n" );
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document.write( "P(A) = P(M, S) + P(O, S) + P(E,S)\r<BR>\n" );
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document.write( "*Interpretation:*  P(A) is the probability that a randomly selected customer purchased a racket with a small (1/4 inch) grip.\r<BR>\n" );
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document.write( "**b) P(Aᶜ):**\r<BR>\n" );
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document.write( "P(Aᶜ) = 1 - P(A)  (This is the complement of event A; the probability that the grip size is *not* 1/4 inch).\r<BR>\n" );
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document.write( "**c) P(B): Oversized head**\r<BR>\n" );
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document.write( "Event B corresponds to all outcomes where the head size is oversized (O).\r<BR>\n" );
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document.write( "P(B) = P(O, S) + P(O, M) + P(O, L)\r<BR>\n" );
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document.write( "**d) Grip size at least 1/2 inch**\r<BR>\n" );
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document.write( "\"At least 1/2 inch\" means medium (M) or large (L) grip sizes.\r<BR>\n" );
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document.write( "P(grip ≥ 1/2) = P(M, M) + P(M, L) + P(O, M) + P(O, L) + P(E,M) + P(E,L)\r<BR>\n" );
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document.write( "**e) Grip size 1/4 inch and oversized head**\r<BR>\n" );
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document.write( "This is the probability of the intersection of events A and B.\r<BR>\n" );
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document.write( "P(A ∩ B) = P(O, S)\r<BR>\n" );
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document.write( "**f) Grip size 1/4 inch or oversized head**\r<BR>\n" );
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document.write( "This is the probability of the union of events A and B.\r<BR>\n" );
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document.write( "P(A ∪ B) = P(A) + P(B) - P(A ∩ B)\r<BR>\n" );
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document.write( "**g) Probability of 1/4 inch grip given midsized head**\r<BR>\n" );
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document.write( "This is a conditional probability.\r<BR>\n" );
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document.write( "P(A | M) = P(A ∩ M) / P(M) = P(M,S) / [P(M,S) + P(M,M) + P(M,L)]\r<BR>\n" );
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document.write( "**h) Independence of events**\r<BR>\n" );
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document.write( "Events A and B are independent if P(A ∩ B) = P(A) * P(B).  Calculate P(A) * P(B) and compare it to the value you got for P(A ∩ B) in part (e).  If they are equal, the events are independent. If they are not equal, the events are dependent.\r<BR>\n" );
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document.write( "**Provide the table, and I'll calculate the specific probabilities for you!**<BR>\n" );
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