document.write( "Question 1022288: Suppose a die is rolled twice and comes up 4 on the first roll. What is the probability that the second roll is also a 4? (Should I use conditional probability or product rule of probability? Anyway, thanks in advance!) \n" ); document.write( "

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\n" ); document.write( "Question:
\n" ); document.write( "Suppose a die is rolled twice and comes up 4 on the first roll. What is the probability that the second roll is also a 4? (Should I use conditional probability or product rule of probability? Anyway, thanks in advance!)
\n" ); document.write( "
\n" ); document.write( "Solution:
\n" ); document.write( "You could use either method, but the results should come up the same.
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\n" ); document.write( "We assume a fair die.
\n" ); document.write( "1. probability product rule:
\n" ); document.write( "Probability that the first one is a four = 1 (already happened)
\n" ); document.write( "probability that the second one is a four = 1/6.
\n" ); document.write( "Product rule: 1*1/6=1/6.
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\n" ); document.write( "2. conditional probability:
\n" ); document.write( "Probability that the first throw is a four = P(4)=1/6
\n" ); document.write( "Probability that the second throw is a four = P(4)=1/6
\n" ); document.write( "Probability that both are fours: P(4∩4)=(1/6)*(1/6) [product rule]
\n" ); document.write( "Probability that the second throw is a four given the first throw is a four
\n" ); document.write( "=P(4|4)=P(4∩4)/P(4)=(1/6)*(1/6)/(1/6)=1/6 as before. \n" ); document.write( "

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