A) A structure has five floors. Each floor will be filled with either 100 or 200

Question

A) A structure has five floors. Each floor will be filled with either 100 or 200 people. For floor 1, the probability of 100 people is 60%. The same statement applies to each of the other floors. B) Repeat part i and ii with the following exception: The probability of 100 people in floor 5 is 80% if there are at most 500 people in the other four floors. The probability of 100 people in floor 5 is only 30% if there are 600 or more people in the other four floors. i. Find the probability of exactly 600 people in the structure. ii. Find the probability of exactly 700 people in the structure. Please include your equations :) A) A structure has five floors. Each floor will be filled with either 100 or 200 people. For floor 1, the probability of 100 people is 60%. The same statement applies to each of the other floors. B) Repeat part i and ii with the following exception: The probability of 100 people in floor 5 is 80% if there are at most 500 people in the other four floors. The probability of 100 people in floor 5 is only 30% if there are 600 or more people in the other four floors. i. Find the probability of exactly 600 people in the structure. ii. Find the probability of exactly 700 people in the structure. Please include your equations :) A) A structure has five floors. Each floor will be filled with either 100 or 200 people. For floor 1, the probability of 100 people is 60%. The same statement applies to each of the other floors. B) Repeat part i and ii with the following exception: The probability of 100 people in floor 5 is 80% if there are at most 500 people in the other four floors. The probability of 100 people in floor 5 is only 30% if there are 600 or more people in the other four floors. i. Find the probability of exactly 600 people in the structure. ii. Find the probability of exactly 700 people in the structure. Please include your equations :)

Explanation / Answer

A)

probability of 100 people is 60% = 0.6

probability of 200 people is 40% = 0.4

For exactly 600 people = there should be one floor with 200 people and the rest with 100 people

P(600 people) = 5C1 * 0.4 * 0.6 * 0.6 * 0.6 * 0.6 = 0.2592

For exactly 700 people = there should be two floor with 200 people and the rest with 100 people

P(700 people) = 5C2 * 0.4 * 0.4 * 0.6* 0.6* 0.6 = 0.346

B)

probability of 100 people in floor 5 is 80% (atmost 500 in other floors)

probability of 100 people in floor 5 is 30% (alteast 600 in other floors)

For exactly 600 people = there should be one floor with 200 people and the rest with 100 people

P(600 people) = 4 * 0.4 * 0.6 * 0.6 * 0.6 * 0.8 + 0.6 * 0.6 * 0.6 * 0.6 * 0.2 = 0.27648 + 0.02592 = 0.3024

For exactly 700 people = there should be two floor with 200 people and the rest with 100 people

P(700 people) = 6 * 0.6 * 0.6 * 0.4 * 0.4 * 0.3 + 4 * 0.4 * 0.6 * 0.6 * 0.6 * 0.2 = 0.10368 + 0.06912 = 0.1728

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