document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=817507>Question 817507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Recall that there are 4 suits - spades, hearts, clubs, and diamonds - in a standard deck of playing cards. Suppose you play a game in which you draw a card, record the suit, replace it, shuffle, and repeat until you have observed 10 cards. Define X = number of hearts observed.\r<BR>\n" );
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document.write( "(a) Show that X is a binomial random variable.\r<BR>\n" );
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document.write( "(b) Find the probability of observing fewer than 4 hearts in this game. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492083 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=492083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose you play a game in which you draw a card, record the suit, replace it, shuffle, and repeat until you have observed 10 cards. Define X = number of hearts observed. <BR>\n" );
document.write( "(a) Show that X is a binomial random variable.<BR>\n" );
document.write( "Binomial with n = 10; p(heart) = 13/52 = 1/4;<BR>\n" );
document.write( "Draw results are independent because each drawn card is replaced.<BR>\n" );
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document.write( "(b) Find the probability of observing fewer than 4 hearts in this game.<BR>\n" );
document.write( "P(0<= x <=3) = binomcdf(10,1/4,3) = 0.7759<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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