Question

1. what is the theoretical probability of drawing a diamond from a standard deck of 52 cards?

a. \\( \frac { 1 3 } { 2 0 } \\)
b. \\( \frac { 1 } { 1 3 } \\)
c. \\( \frac { 1 3 } { 5 2 } \\)
d. \\( \frac { 1 } { 4 } \\)

Explanation:

Step1: Recall the formula for probability

The formula for probability is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).

Step2: Determine the number of favorable and total outcomes

In a standard deck of 52 cards, the number of diamond - suited cards (favorable outcomes) is 13. The total number of cards (total outcomes) is 52.
So, \(P(\text{drawing a diamond})=\frac{13}{52}\).

Step3: Simplify the fraction

\(\frac{13}{52}=\frac{13\div13}{52\div13}=\frac{1}{4}\)

Answer:

D. \(\frac{1}{4}\)