Question

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Part 1
A card is drawn from a​ well-shuffled deck of 52 cards. What is the probability that the card will have a value of 6 and be a face​ card?

Answer 1

To determine the probability of drawing a card that has a value of 6 and is also a face card from a standard deck of 52 cards, we need to understand the definitions of “value of 6” and “face card”.

1. **Cards with a value of 6**: In a standard deck, there are four cards with the value of 6 (6 of Hearts, 6 of Diamonds, 6 of Clubs, and 6 of Spades).

2. **Face cards**: The face cards in a standard deck are the Kings, Queens, and Jacks. There are three face cards in each of the four suits, so there are a total of 12 face cards (3 face cards × 4 suits).

Now we analyze the question:

- A card cannot simultaneously be a value of 6 and a face card. A value of 6 is simply a numbered card and does not fall under face cards, which are specifically Kings, Queens, and Jacks.

Since there are no cards that meet both criteria at the same time (being a value of 6 and also being a face card), the number of favorable outcomes is 0.

To find the probability, we use the formula:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

Substituting the values we have:

\[
\text{Probability} = \frac{0}{52} = 0
\]

Thus, the probability that the card will have a value of 6 and be a face card is **0**.