what is the probability that either a heart or a face card (K Q J) is chosen but the Q of heart is missing from the deck?

To find the probability that either a heart or a face card (K Q J) is chosen, but the Q of heart is missing from the deck, we need to calculate the probability of two separate events:

1. The probability of choosing either a heart card (excluding the Q of hearts)
2. The probability of choosing a face card (excluding the Q of hearts)

To calculate each probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.

1. Probability of choosing a heart card (excluding the Q of hearts):
- Favorable outcomes: There are 12 possible heart cards (excluding the Q of hearts, which is missing from the deck).
- Total possible outcomes: There are 51 cards remaining in the deck (since the Q of hearts is missing).

Therefore, the probability of choosing a heart card is 12/51.

2. Probability of choosing a face card (excluding the Q of hearts):
- Favorable outcomes: There are 3 face cards (K, Q, J) in each suit, so there are 12 face cards in total (excluding the Q of hearts).
- Total possible outcomes: There are 51 cards remaining in the deck (since the Q of hearts is missing).

Therefore, the probability of choosing a face card is 12/51.

Since we are interested in the probability of either a heart or a face card being chosen, we need to consider the overlapping possibilities. In other words, we need to find the probability of the union of the two events.

To calculate the probability of the union of two independent events, we can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)

In this case, the events of choosing a heart card and choosing a face card are independent events. The Q of hearts is excluded in both events, so their intersection (A and B) is an empty set, meaning they have no common outcomes.

Applying the formula, we have:
P(heart or face card excluding Q of hearts) = P(heart) + P(face) - P(heart and face)

P(heart or face card excluding Q of hearts) = (12/51) + (12/51) - 0

Simplifying, we get:
P(heart or face card excluding Q of hearts) = 24/51

Therefore, the probability that either a heart or a face card (excluding the Q of hearts) is chosen is 24/51.