To answer the question about the probabilities when drawing a card from a well-shuffled deck of 52 playing cards, we will consider the following probabilities:
The probability that Wesley draws an ace or a jack is [tex]\(\frac{\text{number of aces} + \text{number of jacks}}{\text{total number of cards}}\)[/tex].
Since there are 4 aces and 4 jacks:
[tex]\(\frac{4 + 4}{52} = \frac{8}{52}\)[/tex].
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\(\frac{8 \div 4}{52 \div 4} = \frac{2}{13}\)[/tex].
Next, the probability that Wesley draws a number card (a card with a number from 2 to 10) is [tex]\(\frac{\text{number of number cards}}{\text{total number of cards}}\)[/tex].
There are 40 number cards in the deck (10 cards for each number from 2 to 10, across 4 suits):
[tex]\(\frac{40}{52}\)[/tex].
We can also simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\(\frac{40 \div 4}{52 \div 4} = \frac{10}{13}\)[/tex].
Therefore, the answers are as follows:
The probability that Wesley draws an ace or a jack is [tex]\(\frac{2}{13}\)[/tex].
The probability that Wesley draws a number card is [tex]\(\frac{10}{13}\)[/tex].
