Probability of Seeing a Sword in 5-Card Hand - 5 Times

[ParisSpart]

Repeat 5 times the following experiment:
Pull 5 cards of 5 common decks(52 cards each deck and one card from each),
note somewhere what hand pulled and repositioned every
cards in the deck from which we got.
What is the probability that we are going to see for first time a sword exactly the last time
we do the experiment?

first of all i found the N(Ω)=from 52 card we take 5 for five times but i can't find the N(A) any ideas?

 

[HallsofIvy]

Repeat 5 times the following experiment:
Pull 5 cards of 5 common decks(52 cards each deck and one card from each),
note somewhere what hand pulled

What do you mean by "what hand pulled"? The precise 5 cards?

and repositioned every
cards in the deck from which we got.
What is the probability that we are going to see for first time a sword exactly the last time
we do the experiment?

first of all i found the N(Ω)=from 52 card we take 5 for five times but i can't find the N(A) any ideas?

`
A "sword" is what I would call a "spade", right? It doesn't really matter- it just a matter of one suit not showing up until the fifth trial.
The probability of drawing a specific suite is 13/52= 1/4 and the probability of NOT drawing it is 1- 3/4= 1/4. In order NOT to have drawn a "sword" in the first four trials you must have drawn 16 consecutive "non-swords". Can you find that probability.

 

[haruspex]

What do you mean by "what hand pulled"? The precise 5 cards?

As I read it, one experiment consists of pulling one card from each of five decks, producing a hand of five cards. The cards are replaced and the experiment repeated four more times, producing 5 hands in all. We want the probability that the last hand contains a spade, but no earlier hand does.

` The probability of drawing a specific suit is 13/52= 1/4 and the probability of NOT drawing it is 1- 3/4= 1/4.

You mean it's 1-1/4 = 3/4.
ParisSpart, what is the probability that a given hand contains no swords?