document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087210>Question 1087210</A>: <I><SPAN STYLE=\"word-break: break-all;\"> there are 3 red and 4white balls in box four balls are selected with replacement from the box. find probability by bernoill trial of event 1 2red ball and 2 white 2 all 4 balls white. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701508 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=701508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question:<BR>\n" );
document.write( "there are 3 red and 4white balls in box four balls are selected with replacement from the box. find probability by bernoill trial of event 1 2red ball and 2 white 2 all 4 balls white.<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "The situation satisfies conditions for a binomial distribution, verified as follows:<BR>\n" );
document.write( "1. Bernoulli trials, i.e. exactly two possible outcomes (red=success, white = failure)<BR>\n" );
document.write( "2. Number of trials is known before and constant throughout the experiment (4), i.e. independent of outcomes.<BR>\n" );
document.write( "3. All trials are independent of each other (satisfied from context)<BR>\n" );
document.write( "4. Probability of success is known, and remain constant throughout trials (P(red)=3/7 balls are replaced)<BR>\n" );
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document.write( "Since all criteria are satisfied, we can model with binomial distribution, where the probability of x successes out of N trials each with probability of success p is given by<BR>\n" );
document.write( "P(x)=C(N,x)(p^x)(1-p)^(N-x)<BR>\n" );
document.write( "and,<BR>\n" );
document.write( "C(N,x) is number of combinations of selecting x objects out of N.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "p=P(red)=3/7<BR>\n" );
document.write( "n=4<BR>\n" );
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document.write( "(a) P(2 red and 2 white) => x=2<BR>\n" );
document.write( "=C(4,2)(3/7)^2(4/7)^2<BR>\n" );
document.write( "=864/2401  [note: fractions give exact probability values]<BR>\n" );
document.write( "=0.35985 approximately<BR>\n" );
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document.write( "(b) P(4 whites)  => x=0<BR>\n" );
document.write( "=C(4,0)(3/7)^0(4/7)^4<BR>\n" );
document.write( "=256/2401<BR>\n" );
document.write( "=0.10662 approximately </SPAN>\n" );
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