Thread: Please could someone explain this probability question!

Question :
Suppose a train driver has a 2% chance of crash during every journey. Can we say that he would be mathematically certain of crash after 45 journeys?


I am trying to apply the combinations formula in this question as a tree diagram would be too time consuming, I am now thinking i am going down the COMPLETELY wrong path! Could anyone please take a few minutes to give me some guidance, thank you!!

If A and B are two events, let denote the event when both A and B occur, and denote the event when either A or B (or both) occur. Then . So, in general the probability of is smaller than the sum of probabilities.

On the other hand, if A and B are independent, then . So, if crashes during different journeys are independent, then the probability that there will be no crash during 45 journeys is .

Hello, Ben91!

Suppose a train driver has a 2% chance of crash during every journey.

Can we say that he would be mathematically certain of crash after 45 journeys?
No!

The key phrase is "every journey".

For each journey: .

We have:
. .

Therefore:
. .

We can never be 100% certain of a crash.

As usual, I was completely over thinking the question! Big thank you to both of you for explaining the question and allowing me to understand