document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191525>Question 1191525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MAT 145: Topics In Contemporary Math<BR>\n" );
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document.write( "1) Suppose we perform an experiment where we pick a two letters: one from the word <BR>\n" );
document.write( "“COBRA” and one from the word “FISH”. What is the sample space of all possible <BR>\n" );
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document.write( "Suppose V is the event that we select exactly one vowel. What are the outcomes in this event?\r<BR>\n" );
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document.write( "Suppose B is the event we select the B from the word COBRA. What are the outcomes in this event?\r<BR>\n" );
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document.write( "What are the outcomes in 𝑉 𝑎𝑛𝑑 𝐵?\r<BR>\n" );
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document.write( "What are the outcomes in 𝑉 𝑜𝑟 𝐵?<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 #849114 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=849114\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to break down this probability problem:\r<BR>\n" );
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document.write( "**1. Sample Space:**\r<BR>\n" );
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document.write( "The sample space consists of all possible pairs of letters, one from each word.  We can represent them as (letter from COBRA, letter from FISH):\r<BR>\n" );
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document.write( "S = {(C, F), (C, I), (C, S), (C, H), (O, F), (O, I), (O, S), (O, H), (B, F), (B, I), (B, S), (B, H), (R, F), (R, I), (R, S), (R, H), (A, F), (A, I), (A, S), (A, H)}\r<BR>\n" );
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document.write( "There are 5 letters in \"COBRA\" and 4 letters in \"FISH\", so the sample space has 5 * 4 = 20 possible outcomes.\r<BR>\n" );
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document.write( "**2. Event V (Exactly One Vowel):**\r<BR>\n" );
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document.write( "V = {(C, I), (O, F), (O, I), (O, S), (O, H), (B, I), (R, I), (A, F), (A, I), (A, S), (A, H)}\r<BR>\n" );
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document.write( "The vowels in \"COBRA\" are O and A, and the vowel in \"FISH\" is I.  Event V includes all pairs where one letter is a vowel and the other is a consonant.\r<BR>\n" );
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document.write( "**3. Event B (Selecting B from COBRA):**\r<BR>\n" );
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document.write( "B = {(B, F), (B, I), (B, S), (B, H)}\r<BR>\n" );
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document.write( "This event includes all pairs where the first letter is B.\r<BR>\n" );
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document.write( "**4. Event V and B (Exactly One Vowel AND Selecting B):**\r<BR>\n" );
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document.write( "V ∩ B = {(B, I)}\r<BR>\n" );
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document.write( "This event includes only the outcome where we select B from \"COBRA\" and I from \"FISH\".\r<BR>\n" );
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document.write( "**5. Event V or B (Exactly One Vowel OR Selecting B):**\r<BR>\n" );
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document.write( "V ∪ B = {(C, I), (O, F), (O, I), (O, S), (O, H), (B, F), (B, I), (B, S), (B, H), (R, I), (A, F), (A, I), (A, S), (A, H)}\r<BR>\n" );
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document.write( "This event includes all outcomes that are in V, or in B, or in both.  We simply combine the outcomes from the two events, without repeating any outcomes.<BR>\n" );
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