You are Here: Home >< Maths

# STEP Probability Choosing Keys watch

1. This is from Siklos' book.

My question is about part (i): I just did it by saying that 1 of the keys has to be the correct one so therefore the probability must be 1/k, since each key is equally likely of being anywhere in the chain and there are k keys in total.

However I don't understand the solution given by the author. Specifically I don't understand where the product given for comes from? Can someone please explain this part?
Attached Images

2. (Original post by FXLander)
This is from Siklos' book.

My question is about part (i): I just did it by saying that 1 of the keys has to be the correct one so therefore the probability must be 1/k, since each key is equally likely of being anywhere in the chain and there are k keys in total.

However I don't understand the solution given by the author. Specifically I don't understand where the product given for comes from? Can someone please explain this part?
You'll kick yourself.

It comes from the line above.

E.g. to succeed on the third attempt, requires it to fail on the first and fail on the second.

P(fail on first) = (k-1)/k

k-1 keys left to try:

P(fail on second) = (k-2)/(k-1)

k-2 keys left.

P(succeed on third) = 1/(k-2)

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 11, 2017
Today on TSR

Get the low down

### University open days

• University of Exeter
Wed, 24 Oct '18
Wed, 24 Oct '18
• Northumbria University
Wed, 24 Oct '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams