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Tongariro Adventures is investigating removing the insurance option due to a low amount of people purchasing insurance. Instead, they will put all bike hiring prices up a small amount.

  • There is an average of 350 adventure bookings (total) made per week
  • An incident involving electric bikes costs $550 on average to fix
  • Day bookings: electric bike hires have an incident rate of 0.02
  • Overnight bookings: electric bike hires have an incident rate of 0.09

Calculate the cost per cyclist increase, of their bike hiring prices. [Note: The price increase does not affect those who provide their own bikes]

I understand that this is the question 3(c) from the 2022 derived grade exam. To answer this question you will have to answer the previous questions as well. There are cyclists booking adventure trips and they are divided into two categories: day and night trips, and each has three subcategories: having their own bike, hiring an electric bike or hiring a standard bike. After completing a probability tree for the previous questions you should have:

Now, we will look into your question. First, we will calculate the proportion of incidents:

For Day trips: 0.7 * 0.25 * 0.02 = 0.0035
For Night trips: 0.3 * 0.33 * 0.09 = 0.00891

Total proportion of incidents out of all trip bookings:
0.0035 + 0.00891 = 0.01241

Expected number of incidents per week (out of 350 bookings):
350 * 0.01241 = 4.3435

Expected average cost of the incidents per week would be:
4.3435 * 550 = 2388.93 ($)

Out of all 350 bookings of the track one out of five cyclists would use their own bike, which we know from (a), so only 4/5 of the 350 bikes would be hired:

350 * 0.8 = 280
So we can distribute this expected average cost of incidents between the 280 bikes:

2388.93/280 = 8.53 ($), or we can round it to $9.