document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198975>Question 1198975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A frequency distribution for the ages of the 40 students (including<BR>\n" );
document.write( "undergraduate and graduate students) in Dr. Chung’s Probability and Statistics<BR>\n" );
document.write( "class is presented in the Table below. <BR>\n" );
document.write( "Age (yr)- Frequency<BR>\n" );
document.write( "17 - 1<BR>\n" );
document.write( "18 - 1<BR>\n" );
document.write( "19 - 9<BR>\n" );
document.write( "20 - 7<BR>\n" );
document.write( "21 - 7<BR>\n" );
document.write( "22 - 5<BR>\n" );
document.write( "23 - 3<BR>\n" );
document.write( "24 - 4<BR>\n" );
document.write( "26 - 1<BR>\n" );
document.write( "35 - 1<BR>\n" );
document.write( "36 - 1<BR>\n" );
document.write( "One student is selected at random. Let<BR>\n" );
document.write( "A = event the student selected is under 21,<BR>\n" );
document.write( "B = event the student selected is over 30,<BR>\n" );
document.write( "C = event the student selected is in his or her 20s, and<BR>\n" );
document.write( "D = event the student selected is over 18.<BR>\n" );
document.write( "Determine probabilities of the following events:<BR>\n" );
document.write( "a) (not D) b) (A & D) c) (A or D) d) (B or C) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848216 by </B><A HREF=/tutors/aboutme.mpl?userid=textot><B>textot(100)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=textot><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=848216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate Total Frequency:**\r<BR>\n" );
document.write( "\n" );
document.write( "* Total number of students = 1 + 1 + 9 + 7 + 7 + 5 + 3 + 4 + 1 + 1 + 1 = 40\r<BR>\n" );
document.write( "\n" );
document.write( "**2. Define Events:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **A:** Student is under 21 (Age <= 20)<BR>\n" );
document.write( "* **B:** Student is over 30 (Age > 30)<BR>\n" );
document.write( "* **C:** Student is in their 20s (Age 20-29)<BR>\n" );
document.write( "* **D:** Student is over 18 (Age > 18)\r<BR>\n" );
document.write( "\n" );
document.write( "**3. Calculate Probabilities:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **P(A):** Probability of student being under 21<BR>\n" );
document.write( "    * P(A) = (1 + 1 + 9 + 7) / 40 = 18/40 = 0.45\r<BR>\n" );
document.write( "\n" );
document.write( "* **P(B):** Probability of student being over 30<BR>\n" );
document.write( "    * P(B) = (1 + 1) / 40 = 2/40 = 0.05\r<BR>\n" );
document.write( "\n" );
document.write( "* **P(C):** Probability of student being in their 20s<BR>\n" );
document.write( "    * P(C) = (7 + 7 + 5 + 3 + 4) / 40 = 26/40 = 0.65\r<BR>\n" );
document.write( "\n" );
document.write( "* **P(D):** Probability of student being over 18<BR>\n" );
document.write( "    * P(D) = (9 + 7 + 7 + 5 + 3 + 4 + 1 + 1 + 1) / 40 = 38/40 = 0.95\r<BR>\n" );
document.write( "\n" );
document.write( "**4. Calculate Probabilities of Compound Events:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **a) P(not D):** Probability of student not being over 18 (i.e., 18 or younger)<BR>\n" );
document.write( "    * P(not D) = 1 - P(D) = 1 - 0.95 = 0.05\r<BR>\n" );
document.write( "\n" );
document.write( "* **b) P(A & D):** Probability of student being under 21 and over 18 (i.e., 19 or 20)<BR>\n" );
document.write( "    * P(A & D) = (9 + 7) / 40 = 16/40 = 0.4\r<BR>\n" );
document.write( "\n" );
document.write( "* **c) P(A or D):** Probability of student being under 21 or over 18 (includes all students except those aged 17 or 18)<BR>\n" );
document.write( "    * P(A or D) = P(A) + P(D) - P(A & D) = 0.45 + 0.95 - 0.4 = 1\r<BR>\n" );
document.write( "\n" );
document.write( "* **d) P(B or C):** Probability of student being over 30 or in their 20s (includes all students except those under 20)<BR>\n" );
document.write( "    * P(B or C) = P(B) + P(C) = 0.05 + 0.65 = 0.7\r<BR>\n" );
document.write( "\n" );
document.write( "**In summary:**\r<BR>\n" );
document.write( "\n" );
document.write( "* a) P(not D) = 0.05<BR>\n" );
document.write( "* b) P(A & D) = 0.4<BR>\n" );
document.write( "* c) P(A or D) = 1<BR>\n" );
document.write( "* d) P(B or C) = 0.7<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );