Question

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 door.If the probabilities with which the group selects the doors are 0.2, 0.1, 0.2, and 0.5, respectively, what is the expected number of hours before the the group exits the building?E[Number of hours]=__________-

Answer 1

Answer:

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!!!