document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84798>Question 84798</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0205459587/algebrahomeworkh>Elementary Statistics in Social Research</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that you purchase a lottery ticket that contains two numbers and a letter such as\r<BR>\n" );
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document.write( "3  7  P\r<BR>\n" );
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document.write( "A. What is the probability that you match the first digit?<BR>\n" );
document.write( "B. What is the probability that you match the second digit?<BR>\n" );
document.write( "C. What is the probability that you do not match the first digit?<BR>\n" );
document.write( "D. What is the probability that you match both the first and second digits?<BR>\n" );
document.write( "E. What is the probability that you match the letter?<BR>\n" );
document.write( "F. what is the probability of a perfect match (both digits and the letter)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61098 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=61098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Presuming that the numbers can be zero through 9 (a total of 10 numbers):<BR>\n" );
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document.write( "A. The probability of matching the first digit is 1 in 10 or 10% or 0.1<BR>\n" );
document.write( "B. Similarly, the probability of matching the second digit is also 1 in 10 or 10% or 0.1<BR>\n" );
document.write( "C. The probability that you do not match the first digit is 9 in 10 or 90% or 0.9<BR>\n" );
document.write( "D. The probability that you do match both the first and second digits is equal to the product <BR>\n" );
document.write( "of the probability of matching the first digit times the probability of matching the second<BR>\n" );
document.write( "digit.  This product is 0.1 times 0.1 and it equals 0.01 or 1 in 100 or 1%. You can look<BR>\n" );
document.write( "at it another way. The first two digits combined could be any number from 00 to 99. This<BR>\n" );
document.write( "is a total of 100 numbers and you therefore have 1 chance in 100 of getting the correct number.<BR>\n" );
document.write( "E. Since there are 26 letters in the alphabet, you have 1 chance in 26 of getting the<BR>\n" );
document.write( "right letter. Dividing 26 into 1 tells you that in decimal form this probability is <BR>\n" );
document.write( "0.038461538 or 3.8461538%<BR>\n" );
document.write( "F. The probability of getting a perfect match is the product of the three probabilities<BR>\n" );
document.write( "for getting each of the numbers and the letter correct. This product is:<BR>\n" );
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document.write( "0.1 * 0.1 * 0.038461538 = 0.0003846153846 or its equivalent percent of 0.03846153846%.<BR>\n" );
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document.write( "You could also get the equivalent by multiplying:<BR>\n" );
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document.write( "(1/10)*(1/10)*(1/26) = 1/2600 <BR>\n" );
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document.write( "which means you have a 1 in 2600 chance of getting all three correct. This also means that<BR>\n" );
document.write( "on average you should get it correct once in every 2600 times you try drawing the numbers<BR>\n" );
document.write( "and the letter.<BR>\n" );
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document.write( "Hope this helps you to understand probability a little better. </SPAN>\n" );
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