Question

Expected value (statistics)

Suppose there is a multiple choice test of 34 questions, each question has 6 options to answer (so p=1/6, only 1 answer is correct). If we assume that 19/34 of the questions should be correct to pass, then how many students is expected to pass if the population is 200?

Answer 1

given data:

correct asnwer probability is 1/6

incorrect asnwer probability is 5/6

Total Question is 34

Answer should be min 19 correct answer

so we have to find out for probability of correct answer >=19

for getting r correct answer is

n= total numer

p = probability for correct answer

q = probability for incorrect answer

Probability for passing = 1- probability for failing

= 1-P(r<19)

= 1 -(P(0)+P(1)+........P(18))

Correctt answer	p^r	q^(n-r)	nCr	probability
0	1	0.002032	1	0.0020316
1	0.166666667	0.002438	34	0.0138149
2	0.027777778	0.002926	561	0.0455890
3	0.00462963	0.003511	5984	0.0972566
4	0.000771605	0.004213	46376	0.1507478
5	0.000128601	0.005055	278256	0.1808973
6	2.14335E-05	0.006066	1344904	0.1748674
7	3.57225E-06	0.00728	5379616	0.1398939
8	5.95374E-07	0.008735	18156204	0.0944284
9	9.9229E-08	0.010483	52451256	0.0545586
10	1.65382E-08	0.012579	131128140	0.0272793
11	2.75636E-09	0.015095	286097760	0.0119037
12	4.59394E-10	0.018114	548354040	0.0045631
13	7.65656E-11	0.021737	927983760	0.0015444
14	1.27609E-11	0.026084	1391975640	0.0004633
15	2.12682E-12	0.031301	1855967520	0.0001236
16	3.5447E-13	0.037561	2203961430	0.0000293
17	5.90784E-14	0.045073	2333606220	0.0000062
18	9.8464E-15	0.054088	2203961430	0.0000012
			P(r<19)	0.9999998

p(r>=19) = 1 - 0.999998

= 0.0000002

students passing (200 students) = 200*p(r>=19)= 200*0.0000002

=0.00004

Students will pass only 0.00004.