Math, asked by stephenhansda552, 1 year ago

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.

Answers

Answered by Agastya0606
0

Given: 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.

To find: The probability that the hotel owner will get Rs. 150 per day by renting the sets.

Solution:

  • Now we have given  4 rooms for rental and they are always occupied and  owner has 3 TV sets available on the rental Rs. 50 per day per set.
  • Case 1: no occupant hires a TV set
  • So he will get no money, then the probability of no money will be:

               2/3 x 2/3 x 2/3 x 2/3 = 16/81

  • Case 2: one occupant hires a TV set
  • So he will get 50 rupees, then the probability of 50 rupees will be:

               4 x 1/3 x 2/3 x 2/3 x 2/3 = 32/81

  • Case 3: two occupants hire a TV set
  • So he will get 100 rupees, then the probability of 100 rupees will be:

               { (4 x 3) / (2 x 1) } x 1/3 x 1/3 x 2/3 x 2/3 = 24/81

  • Case 4: three occupants hire a TV set
  • So he will get 150 rupees, then the probability of 150 rupees will be:

               { (4 x 3 x 2) / (3 x 2 x 1) } x 1/3 x 1/3 x 1/3 x 2/3 = 8/81

  • Case 5: four occupants hire a TV set
  • So he will get 200 rupees, then the probability of 200 rupees will be:

               { (4 x 3 x 2) / (3 x 2 x 1) } x 1/3 x 1/3 x 1/3 x 1/3 = 1/81

  • So  the probability that the hotel owner will get Rs. 150 per day by renting the sets is:

               (8/81) + (1/81) = 9/81 = 1/9

Answer:

           The probability that the hotel owner will get Rs. 150 per day by renting the sets is 1/9

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