In a TV show put up by a local supermarket, a lucky customer is selected to pick one box from four identical boxes, one of which (high-valued box) contains a cheque amounting to 1000 times the purchased amount. The other three boxes (low-valued boxes) each contains a cheque amounting to 10 times the purchase amount.

After the customer has made the selection, the show host selects at random and open one of low-valued boxes not chosen by the customer.

The customer is then offered an option to switch choice by selecting one of the two remaining boxes or keep to the original selection.

In order to help the customer make the right decision, calculate the ratio of the probability of customer winning the 1000 times cheque with a choice-switch, to the probability of customer winning the 1000 times cheque with the original selection.