What is the probability that a total of 2 spades will be chosen

Question

A standard deck of 52 cards contains 13 spades, 13 hearts, 13 diamonds, and 13 clubs. A game is played in which 3 decks of cards are shuffled and placed next to each other. A random card is chosen from Deck 1. If it is a spade, then a random card is selected from Deck 2. If, instead, the card from Deck 1 is not a spade, then a random card is chosen from Deck 2 and a random card is chosen from Deck 3. What is the probability that a total of 2 spades will be chosen?

Answer 1

The chances of picking 2 spades from Decks 1 and 2 (scenario 1) is 1/4*1/4=1/16.

The chances of not picking a spade first then picking two spades from Decks 2 and 3 in scenario 2 is 3/4*1/4*1/4=3/64.

Since the two scenarios are mutually exclusive the probability of either one is 1/16+3/64=7/64.