Mathematics: In a popular tale of wizards and witches, a group of them finds themselves in a room with unmarked doors which change position, making it impossible to determine which door is which when the room is entered or reentered. Suppose that there are 4 doors in the room. One door leads out of the building after 3 hours of travel. The second and third doors return to the room after 3.5 and 5 hours of travel, respectively. The fourth door leads to a dead end, the end of which is a 2.5 hour trip from the

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In a popular tale of wizards and witches, a group

iamsecond235p318rq

26.01.2022

Expected number of hours before the the group exits the building = E[Number of hours] = 3.2 hours

Step-by-step explanation:

Expected value, E(X) is given as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

Let X represent the number of hours before exiting the building taking each door. Note that D = Door

D | X | P(X)

1 | 3.0 | 0.2

2 | 3.5 | 0.1

3 | 5.0 | 0.2

4 | 2.5 | 0.5

E(X) = (3×0.2) + (3.5×0.1) + (5×0.2) + (2.5×0.5) = 3.2 hours

Hope this Helps!!!

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