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Assume that random guesses are made for6multiple-choice questions on a test with5 choices for eachquestion, so that there are n=6trials, each with probability of success(correct)

Assume that random guesses are made for6multiple-choice questions on a test with5 choices for eachquestion, so that there are n=6trials, each with probability of success(correct) given by p=0.20.

Find the probability of no correct answers.

Click on the icon to view the binomial probability table.

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Part 1

The probability of no correct answers is

enter your response here.

(Round to three decimal places asneeded.)

Binomial Probabilities

p

n x 0.01 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.99 x n

2 0 0.98 0.902 0.81 0.64 0.49 0.36 0.25 0.16 0.09 0.04 0.01 0.002 0+ 0 2

1 0.02 0.095 0.18 0.32 0.42 0.48 0.5 0.48 0.42 0.32 0.18 0.095 0.02 1

2 0+ 0.002 0.01 0.04 0.09 0.16 0.25 0.36 0.49 0.64 0.81 0.902 0.98 2

3 0 0.97 0.857 0.729 0.512 0.343 0.216 0.125 0.064 0.027 0.008 0.001 0+ 0+ 0 3

1 0.029 0.135 0.243 0.384 0.441 0.432 0.375 0.288 0.189 0.096 0.027 0.007 0+ 1

2 0+ 0.007 0.027 0.096 0.189 0.288 0.375 0.432 0.441 0.384 0.243 0.135 0.029 2

3 0+ 0+ 0.001 0.008 0.027 0.064 0.125 0.216 0.343 0.512 0.729 0.857 0.97 3

4 0 0.961 0.815 0.656 0.41 0.24 0.13 0.062 0.026 0.008 0.002 0+ 0+ 0+ 0 4

1 0.039 0.171 0.292 0.41 0.412 0.346 0.25 0.154 0.076 0.026 0.004 0+ 0+ 1

2 0.001 0.014 0.049 0.154 0.265 0.346 0.375 0.346 0.265 0.154 0.049 0.014 0.001 2

3 0+ 0+ 0.004 0.026 0.076 0.154 0.25 0.346 0.412 0.41 0.292 0.171 0.039 3

4 0+ 0+ 0+ 0.002 0.008 0.026 0.062 0.13 0.24 0.41 0.656 0.815 0.961 4

5 0 0.951 0.774 0.59 0.328 0.168 0.078 0.031 0.01 0.002 0+ 0+ 0+ 0+ 0 5

1 0.048 0.204 0.328 0.41 0.36 0.259 0.156 0.077 0.028 0.006 0+ 0+ 0+ 1

2 0.001 0.021 0.073 0.205 0.309 0.346 0.312 0.23 0.132 0.051 0.008 0.001 0+ 2

3 0+ 0.001 0.008 0.051 0.132 0.23 0.312 0.346 0.309 0.205 0.073 0.021 0.001 3

4 0+ 0+ 0+ 0.006 0.028 0.077 0.156 0.259 0.36 0.41 0.328 0.204 0.048 4

5 0+ 0+ 0+ 0+ 0.002 0.01 0.031 0.078 0.168 0.328 0.59 0.774 0.951 5

6 0 0.941 0.735 0.531 0.262 0.118 0.047 0.016 0.004 0.001 0+ 0+ 0+ 0+ 0 6

1 0.057 0.232 0.354 0.393 0.303 0.187 0.094 0.037 0.01 0.002 0+ 0+ 0+ 1

2 0.001 0.031 0.098 0.246 0.324 0.311 0.234 0.138 0.06 0.015 0.001 0+ 0+ 2

3 0+ 0.002 0.015 0.082 0.185 0.276 0.312 0.276 0.185 0.082 0.015 0.002 0+ 3

4 0+ 0+ 0.001 0.015 0.06 0.138 0.234 0.311 0.324 0.246 0.098 0.031 0.001 4

5 0+ 0+ 0+ 0.002 0.01 0.037 0.094 0.187 0.303 0.393 0.354 0.232 0.057 5

6 0+ 0+ 0+ 0+ 0.001 0.004 0.016 0.047 0.118 0.262 0.531 0.735 0.941 6

7 0 0.932 0.698 0.478 0.21 0.082 0.028 0.008 0.002 0+ 0+ 0+ 0+ 0+ 0 7

1 0.066 0.257 0.372 0.367 0.247 0.131 0.055 0.017 0.004 0+ 0+ 0+ 0+ 1

2 0.002 0.041 0.124 0.275 0.318 0.261 0.164 0.077 0.025 0.004 0+ 0+ 0+ 2

3 0+ 0.004 0.023 0.115 0.227 0.29 0.273 0.194 0.097 0.029 0.003 0+ 0+ 3

4 0+ 0+ 0.003 0.029 0.097 0.194 0.273 0.29 0.227 0.115 0.023 0.004 0+ 4

5 0+ 0+ 0+ 0.004 0.025 0.077 0.164 0.261 0.318 0.275 0.124 0.041 0.002 5

6 0+ 0+ 0+ 0+ 0.004 0.017 0.055 0.131 0.247 0.367 0.372 0.257 0.066 6

7 0+ 0+ 0+ 0+ 0+ 0.002 0.008 0.028 0.082 0.21 0.478 0.698 0.932 7

8 0 0.923 0.663 0.43 0.168 0.058 0.017 0.004 0.001 0+ 0+ 0+ 0+ 0+ 0 8

1 0.075 0.279 0.383 0.336 0.198 0.09 0.031 0.008 0.001 0+ 0+ 0+ 0+ 1

2 0.003 0.051 0.149 0.294 0.296 0.209 0.109 0.041 0.01 0.001 0+ 0+ 0+ 2

3 0+ 0.005 0.033 0.147 0.254 0.279 0.219 0.124 0.047 0.009 0+ 0+ 0+ 3

4 0+ 0+ 0.005 0.046 0.136 0.232 0.273 0.232 0.136 0.046 0.005 0+ 0+ 4

5 0+ 0+ 0+ 0.009 0.047 0.124 0.219 0.279 0.254 0.147 0.033 0.005 0+ 5

6 0+ 0+ 0+ 0.001 0.01 0.041 0.109 0.209 0.296 0.294 0.149 0.051 0.003 6

7 0+ 0+ 0+ 0+ 0.001 0.008 0.031 0.09 0.198 0.336 0.383 0.279 0.075 7

8 0+ 0+ 0+ 0+ 0+ 0.001 0.004 0.017 0.058 0.168 0.43 0.663 0.923 8

n x 0.01 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.99 x n

p

NOTE: 0+ represents a positive probability less than 0.0005.

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Binomial Probabilities
		p
n	x	0.01	0.05	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	0.95	0.99	x	n
2	0	0.98	0.902	0.81	0.64	0.49	0.36	0.25	0.16	0.09	0.04	0.01	0.002	0+	0	2
	1	0.02	0.095	0.18	0.32	0.42	0.48	0.5	0.48	0.42	0.32	0.18	0.095	0.02	1
	2	0+	0.002	0.01	0.04	0.09	0.16	0.25	0.36	0.49	0.64	0.81	0.902	0.98	2
3	0	0.97	0.857	0.729	0.512	0.343	0.216	0.125	0.064	0.027	0.008	0.001	0+	0+	0	3
	1	0.029	0.135	0.243	0.384	0.441	0.432	0.375	0.288	0.189	0.096	0.027	0.007	0+	1
	2	0+	0.007	0.027	0.096	0.189	0.288	0.375	0.432	0.441	0.384	0.243	0.135	0.029	2
	3	0+	0+	0.001	0.008	0.027	0.064	0.125	0.216	0.343	0.512	0.729	0.857	0.97	3
4	0	0.961	0.815	0.656	0.41	0.24	0.13	0.062	0.026	0.008	0.002	0+	0+	0+	0	4
	1	0.039	0.171	0.292	0.41	0.412	0.346	0.25	0.154	0.076	0.026	0.004	0+	0+	1
	2	0.001	0.014	0.049	0.154	0.265	0.346	0.375	0.346	0.265	0.154	0.049	0.014	0.001	2
	3	0+	0+	0.004	0.026	0.076	0.154	0.25	0.346	0.412	0.41	0.292	0.171	0.039	3
	4	0+	0+	0+	0.002	0.008	0.026	0.062	0.13	0.24	0.41	0.656	0.815	0.961	4
5	0	0.951	0.774	0.59	0.328	0.168	0.078	0.031	0.01	0.002	0+	0+	0+	0+	0	5
	1	0.048	0.204	0.328	0.41	0.36	0.259	0.156	0.077	0.028	0.006	0+	0+	0+	1
	2	0.001	0.021	0.073	0.205	0.309	0.346	0.312	0.23	0.132	0.051	0.008	0.001	0+	2
	3	0+	0.001	0.008	0.051	0.132	0.23	0.312	0.346	0.309	0.205	0.073	0.021	0.001	3
	4	0+	0+	0+	0.006	0.028	0.077	0.156	0.259	0.36	0.41	0.328	0.204	0.048	4
	5	0+	0+	0+	0+	0.002	0.01	0.031	0.078	0.168	0.328	0.59	0.774	0.951	5
6	0	0.941	0.735	0.531	0.262	0.118	0.047	0.016	0.004	0.001	0+	0+	0+	0+	0	6
	1	0.057	0.232	0.354	0.393	0.303	0.187	0.094	0.037	0.01	0.002	0+	0+	0+	1
	2	0.001	0.031	0.098	0.246	0.324	0.311	0.234	0.138	0.06	0.015	0.001	0+	0+	2
	3	0+	0.002	0.015	0.082	0.185	0.276	0.312	0.276	0.185	0.082	0.015	0.002	0+	3
	4	0+	0+	0.001	0.015	0.06	0.138	0.234	0.311	0.324	0.246	0.098	0.031	0.001	4
	5	0+	0+	0+	0.002	0.01	0.037	0.094	0.187	0.303	0.393	0.354	0.232	0.057	5
	6	0+	0+	0+	0+	0.001	0.004	0.016	0.047	0.118	0.262	0.531	0.735	0.941	6
7	0	0.932	0.698	0.478	0.21	0.082	0.028	0.008	0.002	0+	0+	0+	0+	0+	0	7
	1	0.066	0.257	0.372	0.367	0.247	0.131	0.055	0.017	0.004	0+	0+	0+	0+	1
	2	0.002	0.041	0.124	0.275	0.318	0.261	0.164	0.077	0.025	0.004	0+	0+	0+	2
	3	0+	0.004	0.023	0.115	0.227	0.29	0.273	0.194	0.097	0.029	0.003	0+	0+	3
	4	0+	0+	0.003	0.029	0.097	0.194	0.273	0.29	0.227	0.115	0.023	0.004	0+	4
	5	0+	0+	0+	0.004	0.025	0.077	0.164	0.261	0.318	0.275	0.124	0.041	0.002	5
	6	0+	0+	0+	0+	0.004	0.017	0.055	0.131	0.247	0.367	0.372	0.257	0.066	6
	7	0+	0+	0+	0+	0+	0.002	0.008	0.028	0.082	0.21	0.478	0.698	0.932	7
8	0	0.923	0.663	0.43	0.168	0.058	0.017	0.004	0.001	0+	0+	0+	0+	0+	0	8
	1	0.075	0.279	0.383	0.336	0.198	0.09	0.031	0.008	0.001	0+	0+	0+	0+	1
	2	0.003	0.051	0.149	0.294	0.296	0.209	0.109	0.041	0.01	0.001	0+	0+	0+	2
	3	0+	0.005	0.033	0.147	0.254	0.279	0.219	0.124	0.047	0.009	0+	0+	0+	3
	4	0+	0+	0.005	0.046	0.136	0.232	0.273	0.232	0.136	0.046	0.005	0+	0+	4
	5	0+	0+	0+	0.009	0.047	0.124	0.219	0.279	0.254	0.147	0.033	0.005	0+	5
	6	0+	0+	0+	0.001	0.01	0.041	0.109	0.209	0.296	0.294	0.149	0.051	0.003	6
	7	0+	0+	0+	0+	0.001	0.008	0.031	0.09	0.198	0.336	0.383	0.279	0.075	7
	8	0+	0+	0+	0+	0+	0.001	0.004	0.017	0.058	0.168	0.43	0.663	0.923	8
n	x	0.01	0.05	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	0.95	0.99	x	n
		p
NOTE: 0+ represents a positive probability less than 0.0005.