document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194207>Question 1194207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> https://ibb.co/jwFWQpm </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848465 by </B><A HREF=/tutors/aboutme.mpl?userid=proyaop><B>proyaop(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=proyaop><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=848465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I can't directly access and process images, but based on the description of the image you linked (assuming it's the Venn diagram for the tennis club problem), I can help you solve it.\r<BR>\n" );
document.write( "\n" );
document.write( "**Tennis Club Problem**\r<BR>\n" );
document.write( "\n" );
document.write( "**Information:**\r<BR>\n" );
document.write( "\n" );
document.write( "* There are 90 players in the tennis club.<BR>\n" );
document.write( "* 23 are juniors (J).<BR>\n" );
document.write( "* The rest are seniors (S).<BR>\n" );
document.write( "* 34 seniors and 10 juniors are male (M).<BR>\n" );
document.write( "* 8 juniors are left-handed (L), 5 of whom are male.<BR>\n" );
document.write( "* There are 18 left-handed players in total, 4 of whom are female seniors.\r<BR>\n" );
document.write( "\n" );
document.write( "**Task:**\r<BR>\n" );
document.write( "\n" );
document.write( "Calculate the probability of various scenarios related to gender, age group, and handedness.\r<BR>\n" );
document.write( "\n" );
document.write( "**Solution:**\r<BR>\n" );
document.write( "\n" );
document.write( "**i) Venn Diagram Analysis**\r<BR>\n" );
document.write( "\n" );
document.write( "Based on the information, populate the Venn diagram as follows:\r<BR>\n" );
document.write( "\n" );
document.write( "* **Total:** 90 players<BR>\n" );
document.write( "* **Juniors (J):** 23<BR>\n" );
document.write( "    * **Male Juniors (J ∩ M):** 10<BR>\n" );
document.write( "    * **Female Juniors (J ∩ M'):** 13<BR>\n" );
document.write( "    * **Left-handed Juniors (J ∩ L):** 8<BR>\n" );
document.write( "    * **Left-handed Female Juniors (J ∩ L ∩ M'):** 3<BR>\n" );
document.write( "* **Seniors (S):** 67<BR>\n" );
document.write( "    * **Male Seniors (S ∩ M):** 34<BR>\n" );
document.write( "    * **Female Seniors (S ∩ M'):** 33<BR>\n" );
document.write( "    * **Left-handed Seniors (S ∩ L):** 10<BR>\n" );
document.write( "    * **Left-handed Female Seniors (S ∩ L ∩ M'):** 4\r<BR>\n" );
document.write( "\n" );
document.write( "**ii) Probability Calculations**\r<BR>\n" );
document.write( "\n" );
document.write( "**(a) Probability that a male player selected at random is left-handed:**\r<BR>\n" );
document.write( "\n" );
document.write( "* P(L | M) = (Number of left-handed males) / (Total number of males)<BR>\n" );
document.write( "* P(L | M) = (10 + 5) / (10 + 34) <BR>\n" );
document.write( "* P(L | M) = 15 / 44 <BR>\n" );
document.write( "* P(L | M) ≈ 0.3409\r<BR>\n" );
document.write( "\n" );
document.write( "**(b) Probability that a left-handed player selected at random is a female junior:**\r<BR>\n" );
document.write( "\n" );
document.write( "* P(J ∩ M' | L) = (Number of left-handed female juniors) / (Total number of left-handed players)<BR>\n" );
document.write( "* P(J ∩ M' | L) = 3 / 18 <BR>\n" );
document.write( "* P(J ∩ M' | L) = 1/6 <BR>\n" );
document.write( "* P(J ∩ M' | L) ≈ 0.1667\r<BR>\n" );
document.write( "\n" );
document.write( "**(c) Probability that a player selected at random is either a junior or a female:**\r<BR>\n" );
document.write( "\n" );
document.write( "* P(J ∪ M') = P(J) + P(M') - P(J ∩ M')<BR>\n" );
document.write( "    * P(J) = 23/90<BR>\n" );
document.write( "    * P(M') = (Number of females) / (Total players) = (13 + 33) / 90 = 46/90<BR>\n" );
document.write( "    * P(J ∩ M') = (Number of female juniors) / (Total players) = 13/90 \r<BR>\n" );
document.write( "\n" );
document.write( "* P(J ∪ M') = (23/90) + (46/90) - (13/90)<BR>\n" );
document.write( "* P(J ∪ M') = 56/90 <BR>\n" );
document.write( "* P(J ∪ M') ≈ 0.6222\r<BR>\n" );
document.write( "\n" );
document.write( "**(d) Probability that a player selected at random is right-handed:**\r<BR>\n" );
document.write( "\n" );
document.write( "* P(L') = 1 - P(L) <BR>\n" );
document.write( "* P(L') = 1 - (18/90) <BR>\n" );
document.write( "* P(L') = 72/90 <BR>\n" );
document.write( "* P(L') = 0.8\r<BR>\n" );
document.write( "\n" );
document.write( "**(e) Probability that a right-handed player selected at random is not a junior:**\r<BR>\n" );
document.write( "\n" );
document.write( "* P(S | L') = (Number of right-handed seniors) / (Total number of right-handed players)<BR>\n" );
document.write( "* P(S | L') = (34 + 33) / 72 <BR>\n" );
document.write( "* P(S | L') = 67/72 <BR>\n" );
document.write( "* P(S | L') ≈ 0.9306\r<BR>\n" );
document.write( "\n" );
document.write( "**(f) Probability that a right-handed female player selected at random is a junior:**\r<BR>\n" );
document.write( "\n" );
document.write( "* P(J | L' ∩ M') = (Number of right-handed female juniors) / (Total number of right-handed female players)<BR>\n" );
document.write( "* P(J | L' ∩ M') = 13 / 33 <BR>\n" );
document.write( "* P(J | </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );