document.write( "Question 630051: A fair coin tossed 64 times. Find the probability of getting 32 to 40 heads inclusive \n" ); document.write( "
Algebra.Com's Answer #396676 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
this is going to be equal to the probability of getting:
\n" ); document.write( "32 heads + probability of getting
\n" ); document.write( "33 heads + probability of getting
\n" ); document.write( "34 heads + probability of getting
\n" ); document.write( "35 heads + probability of getting
\n" ); document.write( "36 heads + probability of getting
\n" ); document.write( "37 heads + probability of getting
\n" ); document.write( "38 heads + probability of getting
\n" ); document.write( "39 heads + probability of getting
\n" ); document.write( "40 heads.
\n" ); document.write( "since this is a binomial type of probability problem, the formula would be:
\n" ); document.write( "probability of getting x heads = C(n,x) * p^x * q^(n-x)
\n" ); document.write( "n is equal to the number of tosses which is equal to 64
\n" ); document.write( "x is equal to the desired number of heads.
\n" ); document.write( "p is equal to the probability of getting a heads which is equal to .5
\n" ); document.write( "q is equal to the probability of not getting a heads which is also equal to .5 since the total probability of getting a heads and not getting a heads has to be equal to 1.
\n" ); document.write( "C(n,x) is the combination formula of n! / (x! * (n-x)!)
\n" ); document.write( "i cheated by using excel to calculatoe the probbabilities and this is what i got.
\n" ); document.write( "the sum of all the probabilities is supposed to equal 1 which it does so i'm reasonably sure that i did it right.
\n" ); document.write( "
\r\n" );
document.write( "x	C(n,x)	        p^x	        q^(n-x)	        p(n,x)\r\n" );
document.write( "0	1	        1	        5.42101E-20	5.42101E-20\r\n" );
document.write( "1	64	        0.5	        1.0842E-19	3.46945E-18\r\n" );
document.write( "2	2016	        0.25	        2.1684E-19	1.09288E-16\r\n" );
document.write( "3	41664	        0.125	        4.33681E-19	2.25861E-15\r\n" );
document.write( "4	635376	        0.0625	        8.67362E-19	3.44438E-14\r\n" );
document.write( "5	7624512	        0.03125	        1.73472E-18	4.13326E-13\r\n" );
document.write( "6	74974368	0.015625	3.46945E-18	4.06437E-12\r\n" );
document.write( "7	621216192	0.0078125	6.93889E-18	3.36762E-11\r\n" );
document.write( "8	4426165368	0.00390625	1.38778E-17	2.39943E-10\r\n" );
document.write( "9	27540584512	0.001953125	2.77556E-17	1.49298E-09\r\n" );
document.write( "10	1.51473E+11	0.000976563	5.55112E-17	8.21138E-09\r\n" );
document.write( "11	7.43596E+11	0.000488281	1.11022E-16	4.03104E-08\r\n" );
document.write( "12	3.28421E+12	0.000244141	2.22045E-16	1.78038E-07\r\n" );
document.write( "13	1.31369E+13	0.00012207	4.44089E-16	7.12151E-07\r\n" );
document.write( "14	4.78557E+13	6.10352E-05	8.88178E-16	2.59426E-06\r\n" );
document.write( "15	1.59519E+14	3.05176E-05	1.77636E-15	8.64754E-06\r\n" );
document.write( "16	4.88527E+14	1.52588E-05	3.55271E-15	2.64831E-05\r\n" );
document.write( "17	1.37937E+15	7.62939E-06	7.10543E-15	7.47758E-05\r\n" );
document.write( "18	3.60169E+15	3.8147E-06	1.42109E-14	0.000195248\r\n" );
document.write( "19	8.71988E+15	1.90735E-06	2.84217E-14	0.000472706\r\n" );
document.write( "20	1.96197E+16	9.53674E-07	5.68434E-14	0.001063587\r\n" );
document.write( "21	4.1108E+16	4.76837E-07	1.13687E-13	0.002228469\r\n" );
document.write( "22	8.03474E+16	2.38419E-07	2.27374E-13	0.004355644\r\n" );
document.write( "23	1.46721E+17	1.19209E-07	4.54747E-13	0.007953785\r\n" );
document.write( "24	2.50649E+17	5.96046E-08	9.09495E-13	0.013587715\r\n" );
document.write( "25	4.01039E+17	2.98023E-08	1.81899E-12	0.021740344\r\n" );
document.write( "26	6.01558E+17	1.49012E-08	3.63798E-12	0.032610517\r\n" );
document.write( "27	8.46637E+17	7.45058E-09	7.27596E-12	0.045896283\r\n" );
document.write( "28	1.11877E+18	3.72529E-09	1.45519E-11	0.060648659\r\n" );
document.write( "29	1.38882E+18	1.86265E-09	2.91038E-11	0.075287991\r\n" );
document.write( "30	1.62029E+18	9.31323E-10	5.82077E-11	0.087835989\r\n" );
document.write( "31	1.77709E+18	4.65661E-10	1.16415E-10	0.096336246\r\n" );
document.write( "-------------------------------------------------------------------\r\n" );
document.write( "32	1.83262E+18	2.32831E-10	2.32831E-10	0.099346754\r\n" );
document.write( "33	1.77709E+18	1.16415E-10	4.65661E-10	0.096336246\r\n" );
document.write( "34	1.62029E+18	5.82077E-11	9.31323E-10	0.087835989\r\n" );
document.write( "35	1.38882E+18	2.91038E-11	1.86265E-09	0.075287991\r\n" );
document.write( "36	1.11877E+18	1.45519E-11	3.72529E-09	0.060648659\r\n" );
document.write( "37	8.46637E+17	7.27596E-12	7.45058E-09	0.045896283\r\n" );
document.write( "38	6.01558E+17	3.63798E-12	1.49012E-08	0.032610517\r\n" );
document.write( "39	4.01039E+17	1.81899E-12	2.98023E-08	0.021740344\r\n" );
document.write( "40	2.50649E+17	9.09495E-13	5.96046E-08	0.013587715\r\n" );
document.write( "-------------------------------------------------------------------\r\n" );
document.write( "41	1.46721E+17	4.54747E-13	1.19209E-07	0.007953785\r\n" );
document.write( "42	8.03474E+16	2.27374E-13	2.38419E-07	0.004355644\r\n" );
document.write( "43	4.1108E+16	1.13687E-13	4.76837E-07	0.002228469\r\n" );
document.write( "44	1.96197E+16	5.68434E-14	9.53674E-07	0.001063587\r\n" );
document.write( "45	8.71988E+15	2.84217E-14	1.90735E-06	0.000472706\r\n" );
document.write( "46	3.60169E+15	1.42109E-14	3.8147E-06	0.000195248\r\n" );
document.write( "47	1.37937E+15	7.10543E-15	7.62939E-06	7.47758E-05\r\n" );
document.write( "48	4.88527E+14	3.55271E-15	1.52588E-05	2.64831E-05\r\n" );
document.write( "49	1.59519E+14	1.77636E-15	3.05176E-05	8.64754E-06\r\n" );
document.write( "50	4.78557E+13	8.88178E-16	6.10352E-05	2.59426E-06\r\n" );
document.write( "51	1.31369E+13	4.44089E-16	0.00012207	7.12151E-07\r\n" );
document.write( "52	3.28421E+12	2.22045E-16	0.000244141	1.78038E-07\r\n" );
document.write( "53	7.43596E+11	1.11022E-16	0.000488281	4.03104E-08\r\n" );
document.write( "54	1.51473E+11	5.55112E-17	0.000976563	8.21138E-09\r\n" );
document.write( "55	27540584512	2.77556E-17	0.001953125	1.49298E-09\r\n" );
document.write( "56	4426165368	1.38778E-17	0.00390625	2.39943E-10\r\n" );
document.write( "57	621216192	6.93889E-18	0.0078125	3.36762E-11\r\n" );
document.write( "58	74974368	3.46945E-18	0.015625	4.06437E-12\r\n" );
document.write( "59	7624512	        1.73472E-18	0.03125	        4.13326E-13\r\n" );
document.write( "60	7624512	        1.73472E-18	0.03125	        4.13326E-13\r\n" );
document.write( "61	41664	        4.33681E-19	0.125	        2.25861E-15\r\n" );
document.write( "62	2016	        2.1684E-19	0.25	        1.09288E-16\r\n" );
document.write( "-------------------------------------------------------------------\r\n" );
document.write( "63	64	        1.0842E-19	0.5	        3.46945E-18\r\n" );
document.write( "-------------------------------------------------------------------\r\n" );
document.write( "64	1	        5.42101E-20	1	        1.76183E-18\r\n" );
document.write( "

\n" ); document.write( "E-k means the number before the E * 10^-k
\n" ); document.write( "k represents the number following the - sign.
\n" ); document.write( "example
\n" ); document.write( "the probability of getting 63 heads is equal to:
\n" ); document.write( "C(64,63) * (.5)^63 * (.5)^(1) which is equal to:
\n" ); document.write( "C(64,63) * (.5)^63 * (.5)^1 which is equal to 3.46945 * 10^-18
\n" ); document.write( "if you look at the entry for x = 63, you'll see that the probability is 3.46945E-18 which is the same as 3.46945 * 10^-18
\n" ); document.write( "the answer to your question is that the probability of getting 32 to 40 heads inclusive is equal to 0.533290497 which is the sum of the probabilities of getting exactly 32 heads plus exactly 33 heads ..... plus exactly 40 heads.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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