Question

if you randomly select a card from a well - shuffled standard deck of 52 cards, what is the probability that the card you select is a diamond or ace? (your answer must be in the form of a reduced fraction.)
p(diamond or ace) =

Explanation:

Step1: Calculate number of diamonds

There are 13 diamonds in a 52 - card deck.

Step2: Calculate number of aces

There are 4 aces in a 52 - card deck.

Step3: Calculate number of ace - of - diamonds

There is 1 ace - of - diamonds, which is counted in both the diamonds and the aces. We need to avoid double - counting.

Step4: Use the addition rule for probability

The formula for $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$. Here, $A$ is the event of getting a diamond and $B$ is the event of getting an ace. The number of favorable outcomes for $A$ or $B$ is $n(A\ or\ B)=13 + 4-1=16$.

Step5: Calculate the probability

The probability $P=\frac{n(A\ or\ B)}{n(S)}$, where $n(S) = 52$ (total number of cards). So $P=\frac{16}{52}=\frac{4}{13}$.

Answer:

$\frac{4}{13}$