The 8:00 a. m. train has arrived on time 5 days in a row. What's the probability that it will arrive on time tomorrow? Explain.

P = 0.5314

Step-by-step explanation:

As I stated before, the question is incomplete. The answer will be based on this question that I found:

New Jersey Transit claims that its 8:00 a. m. train from Princeton to New York has probability 0.9 of arriving on time. Assume for now that this claim is true.

According to this, we have a 0.9 of chance to arrive on time. Now we want to know the probability that the train arrives on time 6 times in a row.

To know this, is actually easy. Probability of made on time 1 day is 0.90. To get on time two days it would be:

P = 0.90 (day 1) * 0.90 (day 2) = 0.81 or 81%

This is because is the same event to happen the second day. If for example, one of those days, the train was late, then we need to take that factor to the calculations, but the event of getting on time all these days is the same, so the probability to get there is the same for all days and the expression for the independents event is:

P (A∪B) = P (A) * P (B)

That's why I multiply the same number.

Now, as we are going to multiply several days by the same number, we could resume this like this:

P (6 days on time) = 0.9^6

P = 0.5314

This is the probability to arrive on time in the 6th day.