document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183136>Question 183136</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) there are 3 cards in a hat; one is a king,one is a queen and one is an ace. two cards are to be selected at random with replacement using a tree diagram, obtain a smample space for the experiment. then find the probaiblty that a queen and king are selected?\r<BR>\n" );
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document.write( "2) assume that a person spins a spiner and is awarded the amount indicated by the pointer. detrimine the persons expection.<BR>\n" );
document.write( "4 parts<BR>\n" );
document.write( "2-$8<BR>\n" );
document.write( "1-$12 <BR>\n" );
document.write( "1- $1\r<BR>\n" );
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document.write( "3) one card is selected from a deck of cards. find the probabilty of selecting a red card or a card less then 4. (note: the ace is a low card)\r<BR>\n" );
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document.write( "4) a number cube labeled with numbers 1-6 is tossed. what are the odds of the number being less than 3.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137654 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=137654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) there are 3 cards in a hat; one is a king,one is a queen and one is an ace. two cards are to be selected at random with replacement using a tree diagram, obtain a smample space for the experiment. then find the probaiblty that a queen and king are selected? <BR>\n" );
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document.write( "Sample Space:<BR>\n" );
document.write( "1st level of the tree: k,q,a<BR>\n" );
document.write( "2nd level of the tree: k,q,a paired with each element of the 1st level<BR>\n" );
document.write( "(you now have 3*3 = 9 branches<BR>\n" );
document.write( "3rd level of the tree: k,q,a paired with each element of the 2nd level<BR>\n" );
document.write( "(you now have 3*3*3 = 27 branches)<BR>\n" );
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document.write( "Your Problem:<BR>\n" );
document.write( "P(k and q selected in 1st two draws) = 2/9<BR>\n" );
document.write( "(they are kq and qk)<BR>\n" );
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document.write( "2) assume that a person spins a spinner and is awarded the amount indicated by the pointer. determine the persons expected value.<BR>\n" );
document.write( "4 parts<BR>\n" );
document.write( "2-$8<BR>\n" );
document.write( "1-$12 <BR>\n" );
document.write( "1- $1 <BR>\n" );
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document.write( "Random variable values : 8, 12, 1<BR>\n" );
document.write( "Corresponding Probabilities:<BR>\n" );
document.write( "P(8) = 2/4 = 1/2<BR>\n" );
document.write( "P(12) = 1/4<BR>\n" );
document.write( "P(1) = 1/4<BR>\n" );
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document.write( "Multiply each random variable value by it propability and add the products<BR>\n" );
document.write( "to get the expected value:<BR>\n" );
document.write( "E(x) = 8*(1/2) + 12*(1/4) + 1*(1/4) = 4 + 3 + 0.25 = $7.25<BR>\n" );
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document.write( "3) one card is selected from a deck of cards. find the probabilty of selecting a red card or a card less then 4. (note: the ace is a low card) <BR>\n" );
document.write( "P(red or < 4) = P(red) + P(< 4) - P(red AND < 4)<BR>\n" );
document.write( "= 1/2 + 12/52 - (6/52) = 32/52 = 8/13<BR>\n" );
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document.write( "4) a number cube labeled with numbers 1-6 is tossed. what are the odds of the number <BR>\n" );
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document.write( "You did not include the number in your posting.<BR>\n" );
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document.write( "But if it is ANY particular number proceed as follows:<BR>\n" );
document.write( "odds for the number = P(the number) / P(not getting the number) <BR>\n" );
document.write( "= (1/6)/(5/6) = 1/5<BR>\n" );
document.write( "odds for the number are 1:5<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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