Question

Suppose that in West Campus in September of 2019, out of 12 accidents that resulted in trips to Health Services or the emergency room, 4 happened on Friday the 13th. Is this a good reason for my GF Liz, who is very superstitious, to worry that next Friday, December the 13th, 2019, I am particularly in danger in my dorm room in Rich Hall? Just for the sake of this problem, let's pretend that December has only 30 days, so we can compare it with September.

Hint: This is similar to the last one, but the model in question is that we know that 12 accidents occurred in September of 2019, and the probability that any one of them occured on Friday the 13th is the same as any other day, namely 1/30. Therefore the binomial model is X = "how many of the 12 accidents occurred on Friday the 13th?" You want to consider the likelihood of at least 4 accidents on that date.

Answer 1

Given that there were 12 accidents out of which 4 happened on Friday the 13th.

That means, total number accidents,n=12.

Accidents on Friday the 13th is x which can range from 0 to 12.

It is assumed that December has only 30 days.

Therefore, probability of accident occurring on any day of the month = 1/30.

That means, Probability of accident happening on Friday the 13th = 1/30.

Probability of Binomial distribution ,P(X=x)=  

where

Given that last month there were 4 accidents we assume that there will be at least 4 accidents on that day.

That means we need to calculate P(at least 4 accidents)=P(X>=4).

.

or

As the probability is very less, Liz need not worry.