document.write( "Question 888129: A fair pair of dice is rolled 4 times. what is the probability of getting 7 twice? \n" ); document.write( "
Algebra.Com's Answer #537131 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Do you mean getting 7 AT LEAST twice or EXACTLY twice?\r\n" );
document.write( "\r\n" );
document.write( "Either way we first get the probability of getting a seven \r\n" );
document.write( "with just ONE roll of the dice:\r\n" );
document.write( "\r\n" );
document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( "\r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) \r\n" );
document.write( "\r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( "\r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( "\r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) \r\n" );
document.write( "\r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6) \r\n" );
document.write( "\r\n" );
document.write( "That's 6 ways out of 36 or \"6%2F36\" or \"1%2F6\" as the probability\r\n" );
document.write( "of getting seven out with just ONE roll.\r\n" );
document.write( "\r\n" );
document.write( "To get exactly 2 seven rolls out of 4, we use the formula\r\n" );
document.write( "\r\n" );
document.write( "\"%22P%28n%2Cx%3Bp%29%22\"\"%22%22=%22%22\"\"expr%28n%21%2F%28x%21%28n-x%29%21%29%29%2Ap%5Ex%2A%281-p%29%5E%28n-x%29\"\r\n" );
document.write( "\r\n" );
document.write( "with \"n=4\", \"x=2\", \"p=1%2F6\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22P%284%2C2%3B1%2F6%29%22\"\"%22%22=%22%22\"\"expr%284%21%2F%282%21%284-2%29%21%29%29%2A%281%2F6%29%5E2%2A%281-1%2F6%29%5E%284-2%29\"\"%22%22=%22%22\"\"25%2F216\"\"%22%22=%22%22\"\"0.1157407407\"\r\n" );
document.write( "\r\n" );
document.write( "That's the probability of getting exactly 2 sevens.\r\n" );
document.write( "\r\n" );
document.write( "--------------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "To get the probability of 2 or more, calculate the probabilities of\r\n" );
document.write( "\r\n" );
document.write( "exactly 3 and exactly 4 and add them to the above.\r\n" );
document.write( "\r\n" );
document.write( "With a TI-83 or TI-84 calculator, binompdf( is for \"exactly\",\r\n" );
document.write( "binomcdf( is for \"exactly or fewer\")\r\n" );
document.write( "\r\n" );
document.write( "binompdf(4,1/6,2) under 2ND VARS\r\n" );
document.write( "\r\n" );
document.write( "To get probability of 2 or more, 1 minus probability of 1 or fewer:\r\n" );
document.write( "\r\n" );
document.write( "1-binomcdf(4,1/6,1)  get .1319444444 which is \"19%2F144\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );