Question

Enzo is deciding whether to purchase a regular or a standby bus ticket.

Each time Enzo travels on a bus, he either arrives at his destination on time
or is delayed. The standby ticket is less reliable, but it gives Enzo more
value when it does work because it is cheaper.
Enzo collected data on 200 of each type of bus ticket. Once Enzo decides
which type of ticket to purchase, he plans to purchase 10 tickets.
What is Enzo's expected value If he purchases regular tickets?
$
What is Enzo's expected value if he purchases standby tickets?
$
To maximize his expected value, Enzo should purchase standby bus
tickets.
(If necessary, round your answers to the nearest cent.)
The following table shows the value that Enzo gets from each type of ticket
depending on whether he arrives at his destination on time or is delayed.
On time
Delayed
Regular ticket Standby ticket
$20
$40
$5
$15
The following table shows the data Enzo collected on each type of ticket.
Bus status Regular ticket Standby ticket
On time
146
54
200
Delayed
Total
167
33
200

Answer 1

Here is the expected value for each type of ticket:

Regular ticket:

$20 \cdot 0.73 + $5 \cdot 0.27 = $16.60

Standby ticket:

$40 \cdot 0.27 + $15 \cdot 0.73 = $22.10

Therefore, Enzo should purchase standby tickets to maximize his expected value.

Here is the math behind the expected value calculation:

Regular ticket:

$20 \cdot 0.73 + $5 \cdot 0.27 = ($20 \cdot \frac{146}{200}) + ($5 \cdot \frac{54}{200}) = $16.60

Standby ticket:

$40 \cdot 0.27 + $15 \cdot 0.73 = ($40 \cdot \frac{54}{200}) + ($15 \cdot \frac{146}{200}) = $22.10

Explanation: