document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250530>Question 250530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that 5 cards are selected with replacement from a standard deck of 52 playing cards. The <BR>\n" );
document.write( "deck contains 13 denominations (ace, two, three, … , ten, jack, queen, king) of each of four suits <BR>\n" );
document.write( "(hearts, diamonds, spades, and clubs). The kings, queens, and jacks are known as face cards. A card <BR>\n" );
document.write( "is selected and its suit and denomination recorded. The card is replaced in the deck. The deck is <BR>\n" );
document.write( "shuffled, and the process repeated 4 more times. <BR>\n" );
document.write( "a. What is the probability that all five cards are face cards? \r<BR>\n" );
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document.write( "b. What is the probability that at least one card is a face card? \r<BR>\n" );
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document.write( "c. What is the probability that exactly one card is a face card? \r<BR>\n" );
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document.write( "d. What is the probability that no hearts are selected? \r<BR>\n" );
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document.write( "e. What is the probability one or fewer hearts are selected? <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 #182474 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=182474\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that 5 cards are selected with replacement from a standard deck of 52 playing cards. The deck contains 13 denominations (ace, two, three, … , ten, jack, queen, king) of each of four suits (hearts, diamonds, spades, and clubs). The kings, queens, and jacks are known as face cards. <BR>\n" );
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document.write( "A card is selected and its suit and denomination recorded. The card is replaced in the deck. The deck is shuffled, and the process repeated 4 more times.<BR>\n" );
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document.write( "a. What is the probability that all five cards are face cards?<BR>\n" );
document.write( "Since the cards are replaced the selections are independent.<BR>\n" );
document.write( "P(a face card in one draw) = 12/52<BR>\n" );
document.write( "P(5 face cards in 5 draws) = (12/52)^5<BR>\n" );
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document.write( "b. What is the probability that at least one card is a face card?<BR>\n" );
document.write( "P(at least one) = 1 - P(none)<BR>\n" );
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document.write( "P(no face card in 5 draws) = (40/52)^5<BR>\n" );
document.write( "P(at least one face card in 5 draws) = 1 - (40/52)^5<BR>\n" );
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document.write( "c. What is the probability that exactly one card is a face card?<BR>\n" );
document.write( "It's binomial with n= 5 ; p = 12/52, x = 1<BR>\n" );
document.write( "binompdf(5,12/52,1) = 0.4040<BR>\n" );
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document.write( "d. What is the probability that no hearts are selected?<BR>\n" );
document.write( "(3/4)^5<BR>\n" );
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document.write( "e. What is the probability one or fewer hearts are selected?<BR>\n" );
document.write( "binomial with n=5, p= 3/4, 0<= x <=1<BR>\n" );
document.write( "binomcdf(5,3/4,1) = 0.0156<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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