9. There is a biased coin with probability 1/3 for heads and probability 2/3 for

Question

9. There is a biased coin with probability 1/3 for heads and probability 2/3 for tails. Suppose that it is flipped until the third head is obtained. The variance of the number of flips is 18. T0. There are three people who just enter the elevator on the first floor in the South Hall (with five floors). Suppose that each of them chooses a floor among the second floor to the fifth floor randomly and independently of each other. The expected number of floors that the elevator will stop is greater than 2

Explanation / Answer

(10)

Let 'n' denote the number of floors which the elevator can access, and 'k' denote the number of people who are using the lift simultaneously.

The expected number of stops is given by the formula:

E = n*(1-((1-(1/n))^k))

In this case we have:

n = 4, k = 3

Putting values we get:

E = 4*(1-((1-(1/4))^3))

Solving we get:

E = 2.3125

This is greater than 2.

So the answer is TRUE.

Hope this helps !

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