Final answer:
The probability of drawing a 5-card straight flush after having the 2 and 6 of spades is 1/58,800, considering the sequences that can complete the hand.
Step-by-step explanation:
To calculate the probability of drawing a 5-card straight flush from a standard deck of 52 cards after having drawn the 2 of spades and the 6 of spades without replacement, we need to consider the cards that can complete this hand. For a straight flush with these two cards, the only possible sequences include A-2-3-4-5 or 2-3-4-5-6 or 3-4-5-6-7. Since the 2 is already included, the three sequences reduce to A-3-4-5, 3-4-5, and 4-5-6-7.
The three remaining cards need to be the 3, 4, and 5 of spades or the 4, 5, and 7 of spades. There are initially 50 cards left in the deck after the first two have been drawn. The probability of successively drawing the 3, 4, and 5 of spades would be (1/50) * (1/49) * (1/48), and similarly, the probability to draw 4, 5, and 7 of spades would be (1/50) * (1/49) * (1/48). We add these probabilities since either sequence will result in a straight flush.
As a result, the combined probability is 2 * (1/50) * (1/49) * (1/48), because we have two distinct sequences that can complete the straight flush. Simplifying, we get 1/58,800, which is a very low probability.