document.write( "Question 1178463: if three mangoes are taken one after the other from a basket which
\n" ); document.write( "contains 10 ripe and 4 unripe mangoes.\r
\n" ); document.write( "\n" ); document.write( "(a) What is the probability that you will get 3 ripe mangoes?\r
\n" ); document.write( "\n" ); document.write( "(b) What is the probability that you will not get ripe mangoes?\r
\n" ); document.write( "\n" ); document.write( "(c) What is the probability that you will get 1 ripe mangoes? \n" ); document.write( "

Algebra.Com's Answer #807747 by Edwin McCravy(20059) $\"\"$ $\"About$

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if three mangoes are taken one after the other from a basket which contains
\n" ); document.write( "10 ripe and 4 unripe mangoes.\r
\n" ); document.write( "\n" ); document.write( "(a) What is the probability that you will get 3 ripe mangoes?

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document.write( "The probability that you get a ripe mango first is 10 ripe mangos out of 14\r\n" );
document.write( "mangos.  That's 10 out of 14 or 10/14 which reduces to 5/7.\r\n" );
document.write( "The probability that you get a ripe mango second is 9 ripe mangos out of 13\r\n" );
document.write( "mangos.  That's 9 out of 13 or 9/13 which doesn't reduce.\r\n" );
document.write( "The probability that you get a ripe mango third is 8 ripe mangos out of 12\r\n" );
document.write( "mangos.  That's 8 out of 12 or 8/12 which reduces to 2/3.\r\n" );
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document.write( "To succeed you must get a ripe one first AND and ripe one second AND a ripe\r\n" );
document.write( "one third. \"AND\" indicates that we MULTIPLY. So the PRODUCT of those three\r\n" );
document.write( "probabilities is (5/7)(9/13)(2/3) = 30/91.\r\n" );
document.write( "That's the answer.

\n" ); document.write( "(b) What is the probability that you will not get any ripe mangoes?

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document.write( "That means you get 3 unripe mangos.\r\n" );
document.write( "The probability that you get an unripe mango first is 4 unripe mangos out of\r\n" );
document.write( "14 mangos.  That's 4 out of 14 or 4/14 which reduces to 2/7.\r\n" );
document.write( "The probability that you get an unripe mango second is 3 unripe mangos out\r\n" );
document.write( "of 13 mangos.  That's 3 out of 13 or 3/13 which doesn't reduce.\r\n" );
document.write( "The probability that you get an unripe mango third is 2 unripe mangos out of\r\n" );
document.write( "12 mangos.  That's 2 out of 12 or 2/12 which reduces to 1/6.\r\n" );
document.write( "To succeed you must get an unripe one first, AND and unripe one second, AND\r\n" );
document.write( "an unripe one third. \"AND\" indicates that we MULTIPLY. So the PRODUCT of\r\n" );
document.write( "those three probabilities is (5/7)(9/13)(2/3) = 30/91.\r\n" );
document.write( "The PRODUCT of those three probabilities is (2/7)(3/13)(1/6) = 1/91. That's\r\n" );
document.write( "the answer.

\n" ); document.write( "(c) What is the probability that you will get (exactly) 1 ripe mango?

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document.write( "Case 1. You get a ripe mango first, and an unripe mango second and third.\r\n" );
document.write( "The probability that you get a ripe mango first is 10 ripe mangos out of 14\r\n" );
document.write( "mangos.  That's 10 out of 14 or 10/14 which reduces to 5/7.\r\n" );
document.write( "The probability that you get an unripe mango second is 4 unripe mangos out\r\n" );
document.write( "of 13 mangos.  That's 4 out of 13 or 4/13 which doesn't reduce.\r\n" );
document.write( "The probability that you get an unripe mango third is 3 unripe mangos out of\r\n" );
document.write( "12 mangos.  That's 3 out of 12 or 3/12 which reduces to 1/4.\r\n" );
document.write( "To succeed with case 1, you must get a ripe one first AND and an unripe one\r\n" );
document.write( "second AND an unripe one third. \"AND\" indicates that we MULTIPLY. So the\r\n" );
document.write( "PRODUCT of those three probabilities is (5/7)(4/13)(1/4) = 5/91. That's the\r\n" );
document.write( "answer for case 1.\r\n" );
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document.write( "Case 2. You get a ripe mango second, and an unripe mango first and third.\r\n" );
document.write( "That's the same probability as Case 1, or 5/91.\r\n" );
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document.write( "Case 3. You get a ripe mango third, and an unripe mango first and second.\r\n" );
document.write( "That's the same probability as Case 1, or 5/91.\r\n" );
document.write( "\r\n" );
document.write( "To succeed you must have case 1 OR case 2 OR case 3. \"OR\" indicates that we\r\n" );
document.write( "ADD. So the SUM of those three probabilities is 5/91 + 5/91 + 5/91 = 15/91,\r\n" );
document.write( "which does not reduce.  That's the answer.\r\n" );
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document.write( "Edwin

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