document.write( "Question 630570: A biased six-sided die has one face bearing number 3, two faces number 2 and three faces number 1. A boy tosses the die once and observes the number on the uppermost face. He then tosses a number of fair coins equal to the number shown on the die. The random variable X is the number of heads obtained.
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Algebra.Com's Answer #397031 by Edwin McCravy(20062)\"\" \"About 
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A biased six-sided die has one face bearing number 3, two faces number 2 and three faces number 1. A boy tosses the die once and observes the number on the uppermost face. He then tosses a number of fair coins equal to the number shown on the die. The random variable X is the number of heads obtained.
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document.write( "  I. P(1 on die) = 3/6 = 1/2\r\n" );
document.write( "     A. Possible tosses {H,T}\r\n" );
document.write( "     B. P(1 toss 0 heads) = 1/2\r\n" );
document.write( "     C. P(1 toss 1 head) = 1/2\r\n" );
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document.write( " II. P(2 on die) = 2/6 = 1/3\r\n" );
document.write( "     A. Possible tosses {HH,HT,TH,TT}\r\n" );
document.write( "     B. P(2 tosses 0 heads) = 1/4\r\n" );
document.write( "     C. P(2 tosses 1 head)  = 2/4 = 1/2\r\n" );
document.write( "     D. P(2 tosses 2 heads) = 1/4\r\n" );
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document.write( "III. P(3 on die) = 1/6\r\n" );
document.write( "     A. Possible tosses {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}\r\n" );
document.write( "     B. P(3 tosses 0 heads) = 1/8\r\n" );
document.write( "     C. P(3 tosses 1 head)  = 3/8\r\n" );
document.write( "     D. P(3 tosses 2 heads) = 3/8 \r\n" );
document.write( "     E. P(3 tosses 3 heads) = 1/8\r\n" );
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document.write( "P(x=0) = P(D1&H0)+P(D2&H0)+P(D3&H0) = (1/2)(1/2)+(1/3)(1/4)+(1/6)(1/8) = 17/48\r\n" );
document.write( "P(x=1) = P(D1&H1)+P(D2&H1)+P(D3&H1) = (1/2)(1/2)+(1/3)(1/2)+(1/6)(3/8) = 23/48 \r\n" );
document.write( "P(x=2) = P(D2&H2)+P(D3&H2) = (1/3)(1/4)+(1/6)(3/8) = 7/48\r\n" );
document.write( "P(x=3) = P(D3&H3)  = (1/6)(1/8) = 1/48\r\n" );
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document.write( "Probability density function:\r\n" );
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document.write( "  X     P(X)\r\n" );
document.write( "  0     17/48\r\n" );
document.write( "  1     23/48\r\n" );
document.write( "  2      7/48\r\n" );
document.write( "  3      1/48\r\n" );
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document.write( "Note that the probabilities have sum 48/48 or 1\r\n" );
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document.write( "Edwin
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