SOLUTION: 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 mo

Algebra ->  Probability-and-statistics -> SOLUTION: 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 mo      Log On


   

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?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
There are 63 people.
The probability that 0 get the kissing disease is .23^0 * .77^60
The probability that exactly 1 gets the kissing disease is .23^1 * .77^59 * 60! / (1! * 59!)
The probability that exactly 2 get the kissing disease is .23^2 * .77^58 * 60! / (2! * 58!)
The probability that exactly 3 get the kissing disease is .23^3 * .77^57 * 60! / (3! * 57!)
Do this for up to 10 people.
...
The probability that exactly 10 get the kissing disease is .23^10 * .77^50 * 60! / (10! * 50!)

Add up the probabilities of exactly 0 through exactly 10 and you get the probability that no more than 10 gets the kissing disease.

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.




That probability will be, based on the following table:

0.155259513

The table is shown below: 

Number of persons who get kissing disease.
        Number of persons who don't get kissing disease.
                Probability of getting the kissing disease.
                        Probability of not getting the kissing disease.
                                Number of ways that can happen.
                                                        Probability of that number of ways happening.
                                                                        Cumulative probability of that number of ways happening.
0	60	0.23	0.77	1	                1.54683E-07	1.54683E-07
1	59	0.23	0.77	60	                2.77225E-06	2.92693E-06
2	58	0.23	0.77	1770	                2.44282E-05	2.73551E-05
3	57	0.23	0.77	34220	                0.00014107	0.000168425
4	56	0.23	0.77	487635	                0.000600464	0.000768889
5	55	0.23	0.77	5461512	                0.002008824	0.002777713
6	54	0.23	0.77	50063860	        0.005500352	0.008278066
7	53	0.23	0.77	386206920	        0.012674281	0.020952347
8	52	0.23	0.77	2558620845	        0.025081086	0.046033432
9	51	0.23	0.77	14783142660	        0.043285683	0.089319115
10	50	0.23	0.77	75394027566	        0.065940398	0.155259513
11	49	0.23	0.77	342700125300	        0.089529466	0.244788979
12	48	0.23	0.77	1399358844975	        0.109198818	0.353987797
13	47	0.23	0.77	5166863427600	        0.12043506	0.474422857
14	46	0.23	0.77	17345898649800	        0.120770223	0.59519308
15	45	0.23	0.77	53194089192720	        0.110627615	0.705820695
16	44	0.23	0.77	149608375854525	        0.092937972	0.798758667
17	43	0.23	0.77	387221678682300	        0.071851205	0.870609872
18	42	0.23	0.77	925029565741050	        0.051270449	0.921880321
19	41	0.23	0.77	2044802197953900	0.033853215	0.955733536
20	40	0.23	0.77	4191844505805490	0.020729599	0.976463135
21	39	0.23	0.77	7984465725343800	0.011794206	0.988257341
22	38	0.23	0.77	14154280149473100	0.00624522	0.99450256
23	37	0.23	0.77	23385332420868600	0.003082057	0.997584617
24	36	0.23	0.77	36052387482172400	0.00141928	0.999003897
25	35	0.23	0.77	51915437974328300	0.000610475	0.999614372
26	34	0.23	0.77	69886166503903500	0.000245471	0.999859843
27	33	0.23	0.77	88004802264174700	9.23319E-05	0.999952175
28	32	0.23	0.77	103719945525635000	3.25046E-05	0.999984679
29	31	0.23	0.77	114449595062769000	1.07136E-05	0.999995393
30	30	0.23	0.77	118264581564861000	3.30683E-06	0.9999987
31	29	0.23	0.77	114449595062769000	9.55891E-07	0.999999656
32	28	0.23	0.77	103719945525635000	2.58758E-07	0.999999915
33	27	0.23	0.77	88004802264174700	6.55805E-08	0.99999998
34	26	0.23	0.77	69886166503903500	1.55559E-08	0.999999996
35	25	0.23	0.77	51915437974328300	3.45175E-09	0.999999999
36	24	0.23	0.77	36052387482172400	7.16001E-10	1
37	23	0.23	0.77	23385332420868600	1.38727E-10	1
38	22	0.23	0.77	14154280149473100	2.50808E-11	1
39	21	0.23	0.77	7984465725343800	4.22607E-12	1
40	20	0.23	0.77	4191844505805490	6.62725E-13	1
41	19	0.23	0.77	2044802197953900	9.65642E-14	1
42	18	0.23	0.77	925029565741050	        1.30484E-14	1
43	17	0.23	0.77	387221678682300	        1.63154E-15	1
44	16	0.23	0.77	149608375854525	        1.88292E-16	1
45	15	0.23	0.77	53194089192720	        1.99976E-17	1
46	14	0.23	0.77	17345898649800	        1.94781E-18	1
47	13	0.23	0.77	5166863427600	        1.73306E-19	1
48	12	0.23	0.77	1399358844975	        1.40202E-20	1
49	11	0.23	0.77	342700125300	        1.0256E-21	1
50	10	0.23	0.77	75394027566	        6.73963E-23	1
51	9	0.23	0.77	14783142660	        3.94733E-24	1
52	8	0.23	0.77	2558620845	        2.0407E-25	1
53	7	0.23	0.77	386206920	        9.2009E-27	1
54	6	0.23	0.77	50063860	        3.56264E-28	1
55	5	0.23	0.77	5461512	                1.16091E-29	1
56	4	0.23	0.77	487635	                3.09611E-31	1
57	3	0.23	0.77	34220	                6.48991E-33	1
58	2	0.23	0.77	1770	                1.0027E-34	1
59	1	0.23	0.77	60	                1.01528E-36	1
60	0	0.23	0.77	1	                5.05441E-39	1


As far as I know there is no easier way to do this.

It's a lot of grunt work after you figure out what the formula should be.