document.write( "Question 340855: The probability of contracting the kissing disease is .23 when one is exposed to a certain provocative environment. Sixty people are so exposed. What is the probability that no more than 10 are infected with this dreaded disease? \n" ); document.write( "
Algebra.Com's Answer #244154 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
There are 63 people.
\n" ); document.write( "The probability that 0 get the kissing disease is .23^0 * .77^60
\n" ); document.write( "The probability that exactly 1 gets the kissing disease is .23^1 * .77^59 * 60! / (1! * 59!)
\n" ); document.write( "The probability that exactly 2 get the kissing disease is .23^2 * .77^58 * 60! / (2! * 58!)
\n" ); document.write( "The probability that exactly 3 get the kissing disease is .23^3 * .77^57 * 60! / (3! * 57!)
\n" ); document.write( "Do this for up to 10 people.
\n" ); document.write( "...
\n" ); document.write( "The probability that exactly 10 get the kissing disease is .23^10 * .77^50 * 60! / (10! * 50!)\r
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\n" ); document.write( "\n" ); document.write( "Add up the probabilities of exactly 0 through exactly 10 and you get the probability that no more than 10 gets the kissing disease.\r
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\n" ); document.write( "\n" ); document.write( "That becomes the probability of 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10 getting the disease.\r
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\n" ); document.write( "\n" ); document.write( "That probability will be, based on the following table:\r
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\n" ); document.write( "\n" ); document.write( "0.155259513\r
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\n" ); document.write( "\n" ); document.write( "The table is shown below:\r
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document.write( "Number of persons who get kissing disease.\r\n" );
document.write( "        Number of persons who don't get kissing disease.\r\n" );
document.write( "                Probability of getting the kissing disease.\r\n" );
document.write( "                        Probability of not getting the kissing disease.\r\n" );
document.write( "                                Number of ways that can happen.\r\n" );
document.write( "                                                        Probability of that number of ways happening.\r\n" );
document.write( "                                                                        Cumulative probability of that number of ways happening.\r\n" );
document.write( "0	60	0.23	0.77	1	                1.54683E-07	1.54683E-07\r\n" );
document.write( "1	59	0.23	0.77	60	                2.77225E-06	2.92693E-06\r\n" );
document.write( "2	58	0.23	0.77	1770	                2.44282E-05	2.73551E-05\r\n" );
document.write( "3	57	0.23	0.77	34220	                0.00014107	0.000168425\r\n" );
document.write( "4	56	0.23	0.77	487635	                0.000600464	0.000768889\r\n" );
document.write( "5	55	0.23	0.77	5461512	                0.002008824	0.002777713\r\n" );
document.write( "6	54	0.23	0.77	50063860	        0.005500352	0.008278066\r\n" );
document.write( "7	53	0.23	0.77	386206920	        0.012674281	0.020952347\r\n" );
document.write( "8	52	0.23	0.77	2558620845	        0.025081086	0.046033432\r\n" );
document.write( "9	51	0.23	0.77	14783142660	        0.043285683	0.089319115\r\n" );
document.write( "10	50	0.23	0.77	75394027566	        0.065940398	0.155259513\r\n" );
document.write( "11	49	0.23	0.77	342700125300	        0.089529466	0.244788979\r\n" );
document.write( "12	48	0.23	0.77	1399358844975	        0.109198818	0.353987797\r\n" );
document.write( "13	47	0.23	0.77	5166863427600	        0.12043506	0.474422857\r\n" );
document.write( "14	46	0.23	0.77	17345898649800	        0.120770223	0.59519308\r\n" );
document.write( "15	45	0.23	0.77	53194089192720	        0.110627615	0.705820695\r\n" );
document.write( "16	44	0.23	0.77	149608375854525	        0.092937972	0.798758667\r\n" );
document.write( "17	43	0.23	0.77	387221678682300	        0.071851205	0.870609872\r\n" );
document.write( "18	42	0.23	0.77	925029565741050	        0.051270449	0.921880321\r\n" );
document.write( "19	41	0.23	0.77	2044802197953900	0.033853215	0.955733536\r\n" );
document.write( "20	40	0.23	0.77	4191844505805490	0.020729599	0.976463135\r\n" );
document.write( "21	39	0.23	0.77	7984465725343800	0.011794206	0.988257341\r\n" );
document.write( "22	38	0.23	0.77	14154280149473100	0.00624522	0.99450256\r\n" );
document.write( "23	37	0.23	0.77	23385332420868600	0.003082057	0.997584617\r\n" );
document.write( "24	36	0.23	0.77	36052387482172400	0.00141928	0.999003897\r\n" );
document.write( "25	35	0.23	0.77	51915437974328300	0.000610475	0.999614372\r\n" );
document.write( "26	34	0.23	0.77	69886166503903500	0.000245471	0.999859843\r\n" );
document.write( "27	33	0.23	0.77	88004802264174700	9.23319E-05	0.999952175\r\n" );
document.write( "28	32	0.23	0.77	103719945525635000	3.25046E-05	0.999984679\r\n" );
document.write( "29	31	0.23	0.77	114449595062769000	1.07136E-05	0.999995393\r\n" );
document.write( "30	30	0.23	0.77	118264581564861000	3.30683E-06	0.9999987\r\n" );
document.write( "31	29	0.23	0.77	114449595062769000	9.55891E-07	0.999999656\r\n" );
document.write( "32	28	0.23	0.77	103719945525635000	2.58758E-07	0.999999915\r\n" );
document.write( "33	27	0.23	0.77	88004802264174700	6.55805E-08	0.99999998\r\n" );
document.write( "34	26	0.23	0.77	69886166503903500	1.55559E-08	0.999999996\r\n" );
document.write( "35	25	0.23	0.77	51915437974328300	3.45175E-09	0.999999999\r\n" );
document.write( "36	24	0.23	0.77	36052387482172400	7.16001E-10	1\r\n" );
document.write( "37	23	0.23	0.77	23385332420868600	1.38727E-10	1\r\n" );
document.write( "38	22	0.23	0.77	14154280149473100	2.50808E-11	1\r\n" );
document.write( "39	21	0.23	0.77	7984465725343800	4.22607E-12	1\r\n" );
document.write( "40	20	0.23	0.77	4191844505805490	6.62725E-13	1\r\n" );
document.write( "41	19	0.23	0.77	2044802197953900	9.65642E-14	1\r\n" );
document.write( "42	18	0.23	0.77	925029565741050	        1.30484E-14	1\r\n" );
document.write( "43	17	0.23	0.77	387221678682300	        1.63154E-15	1\r\n" );
document.write( "44	16	0.23	0.77	149608375854525	        1.88292E-16	1\r\n" );
document.write( "45	15	0.23	0.77	53194089192720	        1.99976E-17	1\r\n" );
document.write( "46	14	0.23	0.77	17345898649800	        1.94781E-18	1\r\n" );
document.write( "47	13	0.23	0.77	5166863427600	        1.73306E-19	1\r\n" );
document.write( "48	12	0.23	0.77	1399358844975	        1.40202E-20	1\r\n" );
document.write( "49	11	0.23	0.77	342700125300	        1.0256E-21	1\r\n" );
document.write( "50	10	0.23	0.77	75394027566	        6.73963E-23	1\r\n" );
document.write( "51	9	0.23	0.77	14783142660	        3.94733E-24	1\r\n" );
document.write( "52	8	0.23	0.77	2558620845	        2.0407E-25	1\r\n" );
document.write( "53	7	0.23	0.77	386206920	        9.2009E-27	1\r\n" );
document.write( "54	6	0.23	0.77	50063860	        3.56264E-28	1\r\n" );
document.write( "55	5	0.23	0.77	5461512	                1.16091E-29	1\r\n" );
document.write( "56	4	0.23	0.77	487635	                3.09611E-31	1\r\n" );
document.write( "57	3	0.23	0.77	34220	                6.48991E-33	1\r\n" );
document.write( "58	2	0.23	0.77	1770	                1.0027E-34	1\r\n" );
document.write( "59	1	0.23	0.77	60	                1.01528E-36	1\r\n" );
document.write( "60	0	0.23	0.77	1	                5.05441E-39	1\r\n" );
document.write( "
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\n" ); document.write( "\n" ); document.write( "As far as I know there is no easier way to do this.\r
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\n" ); document.write( "\n" ); document.write( "It's a lot of grunt work after you figure out what the formula should be. \n" ); document.write( "
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