Question

Each day your friend goes to NYU, she has a 30% probability of buying a falafel platter for $6, a 50% probability of buying iced coffee for $4, and a 4% chance of riding a taxi home for $25. Over the course, of a month, she travels to NYU on twenty days.

Let F be the amount of money she spends on falafel in a month, C the amount she spends on coffee, and T the amount she spends on taxis.
(a) Find E[F]
(b) Find E[T]
(c) Find E[C]
(d) Find E[F + C + T]

Answer 1

(a) $54

(b) $60

(c) $30

(d) $6.3

Explanation:

Suppose a month has 30 days. Then the expected expense for the whole month is 30 times the expected expense at each day

(a) E[F] = 30*30%*$6 = 30*0.3*6 = $54

(b) E[T] = 30*50%*$4 = 30*0.5*4 = $60

(c) E[C] = 30*4%*$25 = 30*0.04*25 = $30

(d) Suppose all events are independent, the probability that she would spend on all 3 items on the same day is

P[F+T+C] = 0.3*0.5*0.04 = 0.006

So the expected expense she would make on all 3 items is

E[F+T+C] = 30*0.006*(6+4+25) = $6.3