The problem displayed asks for the probability of selecting the card with the number 7 when a card is drawn randomly from the set of cards numbered 4, 5, 6, and 7.

To calculate the probability $P(7)$, we use the formula:

$P(7) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

• The total number of outcomes (total number of cards) is 4 (cards 4, 5, 6, and 7).
• The number of favorable outcomes (the card with the number 7) is 1.

Thus, the probability $P(7)$ is:

$P(7) = \frac{1}{4}$

To express this as a percentage, we convert $\frac{1}{4}$ to a percentage:

$P(7) = \frac{1}{4} \times 100 = 25\%$

So, the probability of picking the card with the number 7 is 25%.

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What is the probability of selecting the card with the number 6?
2. How do probabilities change if you add more cards to the deck?
3. What is the probability of selecting a number less than 6 from this set?
4. How would the probability change if there were two 7s in the deck?
5. Can you explain why the sum of probabilities for all outcomes equals 100%?

Tip: When dealing with simple probability problems, always ensure you account for both the favorable outcomes and the total number of possible outcomes to avoid mistakes.