Question

From a standard deck, what is the probability of picking a card at random with a six or a face card?

standard deck of cards

Question 16 options:

3/13


4/13


7/13


2/13

Answer 1

To determine the probability of picking a card that is either a six or a face card from a standard deck of 52 cards, we first identify how many such cards are there in the deck:

1. **Sixes**: There are 4 sixes in a deck (one for each suit: hearts, diamonds, clubs, spades).

2. **Face cards**: Face cards consist of kings, queens, and jacks. There are 3 face cards per suit and 4 suits, so:
- Total face cards = \(3 \text{ face cards/suit} \times 4 \text{ suits} = 12 \text{ face cards}\).

Now, we sum the number of successful outcomes:

- Total number of sixes = 4
- Total number of face cards = 12

Now, we add these two numbers together to find the total number of desired outcomes:

\[
\text{Total desired outcomes} = 4 \text{ (sixes)} + 12 \text{ (face cards)} = 16
\]

Next, we find the total number of cards in the deck, which is 52.

Finally, we calculate the probability \(P\) of picking a card that is either a six or a face card:

\[
P = \frac{\text{Number of desired outcomes}}{\text{Total number of outcomes}} = \frac{16}{52}
\]

We can simplify this fraction:

\[
P = \frac{16 \div 4}{52 \div 4} = \frac{4}{13}
\]

Thus, the probability of picking a card at random that is either a six or a face card is \(\frac{4}{13}\).

So, the correct answer is:

**4/13**