You are Here: Home >< Maths

# Probability question involving a lift Watch

1. Dear friends,

I am stuck at the following probability problem. Will appreciate your help.

An office block has five floors (ground, 1, 2, 3 and 4), all connected by a lift. When it goes up to any floor (except 4), the probability that after it has stopped it will continue to rise is 3/4. When it goes down to any floor (except the ground floor), the probability that after it has stopped it will continue to go down is 1/4. The lift stops at any floor it passes.

The lift is currently at the first floor having just descended. Calculate the probability of the following events:

a) its second stop is the third floor
b) its third stop is the fourth floor
c) its fourth stop is the first floor.

For part (a), I did this: P(first stop is the second floor)*P(second stop is the third floor) = (3/4)(3/4) = 9/16

For part (b), I did this:

P(first stop is the second floor)*P(second stop is the third floor)*P(third stop is the fourth floor)

= (3/4)(3/4)(3/4) = 27/64

Since the lift is going up and continuing to rise after it stopped at each floor from first floor, finding answers to part (a) and (b) was easy, even though unsure whether my logic is sensible or not. Somehow the answers for part (a) and (b) are correct according to the book. If my methods and answers are incorrect, let me know.

Now, I am really stuck at part (c). Not understanding how to solve the problem. How will the lift’s fourth stop be the first floor if the lift is continuing to rise from first floor and start descending from the fourth floor? Let me know where the mistake is.

2. I think the trick may be that (a), (b) and (c) are completely separate sequences of events. That way, (c) doesn't have to be regarded as an increment to (b).

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: September 19, 2016
Today on TSR

### Should I ask for his number?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• 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

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE