Question

Among a transport department 16 trucks, 5 emit excessive
amount of smoke. If eight of the trucks are randomly selected
for inspection, what is the probability that this sample will
include at least 4 of the trucks, which emit excessive amount of
smoke?
(a) 0.1
(b) 0.141
(c) 0.158
(d) None of these​

Answer 1

Given : Among a transport department 16 trucks, 5 emit excessive

amount of smoke. If eight of the trucks are randomly selected

for inspection,

To find : what is the probability that this sample will  include at least 4 of the trucks, which emit excessive amount of  smoke?

Solution:

Total Trucks = 16

emit excessive  amount of smoke  E = 5

Does not emit excessive  amount of smoke N =11

Number of ways of selecting 8 trucks = ¹⁶C₈  =  12870

at least 4 of the trucks, which emit excessive amount of

smoke = 4E4N  , 5E3N

⁵C₄¹¹C₄ +  ⁵C₅¹¹C₃

=   1650 + 165

= 1815

Probability that this sample will  include at least 4 of the trucks, which emit excessive amount of  smoke  = 1815/12870

= 11/78

= 0.141

0.141   - option b is correct.

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