Final answer:
The probability of drawing the ace of spades from a standard deck is 1/52. In bridge, the probability of a hand without hearts is calculated using combinations. Drawing with replacement keeps card probabilities constant, whereas without replacement changes them after each draw.
Step-by-step explanation:
The question asks about the probability of drawing a specific type of card from a standard deck. In a standard 52-card deck, there is only one ace of spades, making the probability of drawing this card exactly 1 in 52, or P(ace of spades) = 1/52. However, the question seems to have a typo stating P(ace of spades) = 1/26 which is incorrect.
Now, considering the probability of being dealt a hand without any hearts in a bridge hand of 13 cards, we must first acknowledge that there are 39 non-heart cards in the deck. The number of ways to choose 13 cards from the non-hearts is represented by the combination 39C13. The total number of bridge hands possible from the entire deck is 52C13. Therefore, the probability is calculated as the ratio of these two combinations: P(no heart) = 39C13 / 52C13.
For the sampling questions from the deck, when cards are drawn without replacement, the outcomes reflect the continuous removal of cards from the deck, altering the subsequent probabilities with each draw. On the other hand, when sampling with replacement, each draw is independent and the probability for each card remains constant, as the deck is returned to its original state before each draw.
In gambling scenarios, it's important to understand that the expected value of a game can help determine whether or not it is advisable to play. The expected value is calculated by multiplying each possible outcome by its probability and summing these values.