To determine the theoretical probability that Margaret will choose a jack when choosing first from a standard deck of 52 cards, let's go through the solution step-by-step.
1. Identify the Total Number of Cards:
A standard deck has a total of 52 cards.
2. Identify the Number of Jacks:
Within these 52 cards, there are 4 jacks (one from each suit: spades, hearts, diamonds, and clubs).
3. Determine the Probability of Selecting a Jack:
To determine the probability of selecting a jack on the first draw, we divide the number of jacks by the total number of cards.
The formula for probability is:
[tex]\[
P(\text{Jack}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
4. Apply the Numbers to the Formula:
Here, the number of favorable outcomes (selecting a jack) is 4, and the total number of possible outcomes (cards) is 52. Thus, the probability is:
[tex]\[
P(\text{Jack}) = \frac{4}{52}
\][/tex]
5. Simplify the Fraction:
Simplifying [tex]\(\frac{4}{52}\)[/tex] involves dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[
\frac{4}{52} = \frac{4 \div 4}{52 \div 4} = \frac{1}{13}
\][/tex]
So, the theoretical probability that Margaret will choose a jack when choosing first is:
[tex]\[
\frac{1}{13}
\][/tex]
Thus, the correct answer is:
[tex]\[
\frac{1}{13}
\][/tex]
