A hotel has 4 rooms for rental and they are always occupied. The owner has 3 TV sets available on

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23 Mar 2010 TV rent

A hotel has 4 rooms for rental and they are always occupied. The owner has 3 TV sets available on the rental Rs. 50 per day per set.
Only one set will be supplied to one occupant if he wants it. The chance that an occupant will want to hire a set is 1/3.
Find the probability that the hotel owner will get Rs. 150 per day by renting the sets.

OPtion

1) 1/81
2) 2/9
3) 8/81
4) 1/9
5) 16/81
6) 32/81
7) 8/27
8) 5/27
9) 2/5
10) 3/28

Solution

If no occupant hires a TV set, the probability of getting 0 rupee is
2/3*2/3*2/3*2/3 = 16/81

If one occupant hires a TV set, the probability of getting 50 rupee is
[4]*1/3*2/3*2/3*2/3 = 32/81

If two occupants hire a TV set, the probability of getting 100 rupee is

[(4*3)/(2*1)]*1/3*1/3*2/3*2/3 = 24/81

If three occupants hire a TV set, the probability of getting 150 rupee is
[(4*3*2)/(3*2*1)]*1/3*1/3*1/3*2/3 = 8/81

If four occupants want to hire a TV set, the probability of getting 150 rupee is [(4*3*2)/(3*2*1)]*1/3*1/3*1/3*1/3 = 1/81

Hence required probability is (8/81) + (1/81) = 9/81 = 1/9

Correct Option: 4 Best Solution (3)

Dr.Dipin Singh   14 years AGO

4C3 * 1/3 * 1/3 * 1/3 * 2/3 +1/81= 9/81=1/9

Like? Yes (1) | No   

Dimple   14 years AGO

4*(1/3)^3*(2/3) + (1/3)^4 = 1/9

Like? Yes (1) | No   

Dr. Divya   14 years AGO

(4 * 1/3 * 1/3 * 1/3 * 2/3)+1/81 = 1/9

Like? Yes (1) | No