A certain university has 7 vehicles available for use by faculty and staff. Six

Question

A certain university has 7 vehicles available for use by faculty and staff. Six of these are vans and 1 are cars. On a particular day, only two requests for vehicles have been made. Suppose that the two vehicles to be assigned are chosen in a completely random fashion from among the 7.

(a) Let E denote the event that the first vehicle assigned is a van. What is P(E)?


(b) Let F denote the probability that the second vehicle assigned is a van. What is P(F | E)?


(c) Use the results of Parts (a) and (b) to calculate P(E and F) (Hint: Use the definition of P(F | E).)

Explanation / Answer

a) here P(E) =selecting one van out of 6 from 7 vehicles =6/7

b) probability that second vehilce is Van given first Vehicle is Van P(F|E) =selecting one van out of remaining 5 Vans from remaining 6 vehilces =5/6

c) hence P(E and F) =P(E)*P(F|E) =(6/7)*(5/6) =5/7

please revert for any clarification

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