Binomial Probability Questions

#1
For the delivery process, there are 25 delivery vehicles available, of which 23 is required to be operating at any time to give reliable service. During the past 1560 days, the number of days that there was only 23 vehicles available was 190 days, only 22 vehicles available was 22 days, only 21 vehicles available was 3 days and 20 vehicles available only once.
There are also 27 drivers, who each work an 8 hour shift per day. During the past 1560 days, the number of days that there were only 23 drivers available was 95 days, only 22 drivers available was 6 days and only 21 drivers available, once only.

Estimate on how many days per year we should expect reliable delivery times, given the information above. If we increased our number of vehicles by one to 27, how many days per year we should expect reliable delivery times?

I am allowed to assume the probability of a vehicle failure can stay the same when vehicles are increased to 27.
I would like some help on how to calculate the probability of vehicle failure given the sample above. Also I am not sure how the drivers will have an impact. Should I use Rstudio to compute these probabilities? Like to find the root of the dbinom, using uniroot()
 

katxt

Active Member
#2
Estimate on how many days per year we should expect reliable delivery times
This sounds easy but perhaps it's hard.
You need 23 or more vehicles and 23 or more drivers.
Calculate the number of days when you have 23 or more vehicles and make it into a proportion of 1560.
Repeat for the drivers.
Assume independence and multiply your proportions. Find that proportion of a year.