Question

In India, roughly 68.84% of the population live in areas that are roughly designated as rural. In addition, only 67% of the rural population have access to the grid while 94% of the non-rural population have access to power grid.

(a) What is the probability that anybody has access to the grid? Show evidence.

(b) What is the probability that a person lives either in a non-rural area, or has access to the grid or both? Show evidence.

(c) Are the events ‘non-rural’ and ‘access to the grid’ collectively exhaustive? Show evidence.

(d) The event ‘no access to the grid rural population’ is the complement of the event ‘non-rural access to the grid’.   T / F Show evidence.

(e) The problem claims that 67% of the rural population has access to the power grid. If a sample of 10 rural families are selected to receive free computers for their children to use for school-work, what is the probability that 8 families can connect to the grid?

(f) On average, load shedding (losing power) occurs 1 time in a period of 24 hours for people on the grid in a rural area. What is the probability that they will not lose power even once in the next hour while the kids must complete their homework using internet resources?

Answer 1

rural population =68.84%

non-rural population =100-68.84=31.16%

rural population access to grid=67% of 68.84%=46.1228%

rural population not access to grid=68.84-46.1228=22.7172%

non-rural population access to grid=94% of 31.16%=29.2904%

non-rural population not access to grid=31.16-29.2904=1.8696%

A) probability of access of grid=46.1228+29.2904=75.4132%

B)

P(either in a non-rural area, or has access to the grid or both)=31.16+75.4132 - 29.2904=

77.2828%

C)

exhaustive events are those which together cover all the possibilities(100%)

since non rural and access to grid does not cover the possibility of rural population who don not have access to grid. so these are not collectively exhaustive events

D)no access to the grid rural population=22.7172%

non-rural access to the grid =29.2904%

together they does not cover all possibility,there are other possibility of hapenening other than given two.so,

these are not complement to each other

so, given statement is false