Question

a deck of cards contains 52 cards, divided into 13 clubs, 13 diamonds, 13 hearts, and 13 spades. if a dealer deals 6 spades in a row (without replacement), what is the probability that the next card dealt is a spade?

Answer 1

After dealing 6 spades from a deck of 52 cards without replacement, the probability of the next card being a spade is 7/46, as there are 7 spades left out of 46 remaining cards.

Step-by-step explanation:

The question pertains to the probability of drawing a spade from a standard deck of 52 cards after having already dealt 6 spades in a row without replacement. Initially, there are 13 spades in a deck. After dealing 6, there are now 7 spades left. The total number of remaining cards in the deck is 52 - 6 = 46. The probability of the next card being a spade is therefore the number of remaining spades divided by the total number of remaining cards, which is 7/46.

To calculate the probability of an event where there is no replacement, we always adjust the total number of possible outcomes as each event occurs. In this case, 6 cards have been removed, so the deck has 46 cards left, among which 7 are spades. Hence, the probability that the next card dealt is a spade is simply the number of spades left divided by the number of cards left.