Astandard deck of 52 cards is dealt into four hands of 13 cards among four players: north, east, south, and west. what is the ratio of the probability that north and south have none of the 13 spades, to the probability that they have all 13 spades?

The ratio is 1:1

Step-by-step explanation:

The number of ways in which we can choose k element from a group of n elements is calculate using the following equation:

So, there are 52C26 ways to assign 26 cards to the North and South, 13 for each one from a group of 52 cards and there are 39C26 ways to assign 26 cards to the North and South from 39 that are not spades.

Then, the probability P1 that North and South have none of the 13 spades is:

On the other hand, the probability that North and South have all 13 spades it equal to the probability that East and West have none of the 13 spades.

So, there are 52C26 ways to assign 26 cards to the East and West, 13 for each one from a group of 52 cards and there are 39C26 ways to assign 26 cards to the East and West from 39 that are not spades.

Then, The probability P2 that East and West have none of the 13 spades is:

Taking into account that probabilities P1 and P2 are the same, the ratio of the probability that North and South have none of the 13 spades, to the probability that they have all 13 spades is 1:1

step-by-step explanation: