Question

type the correct answer in the box. if necessary, use / for the fraction bar. give your answer in reduced form. a card is drawn at a random from a well - shuffled deck of playing cards. the probability that the card drawn is an ace or a red card is

Explanation:

Step1: Determine total number of cards

A standard deck has 52 cards, so total number of outcomes $n(S)=52$.

Step2: Calculate number of red cards and aces

There are 26 red cards ($n(R)=26$) and 4 aces ($n(A)=4$). But 2 aces are red, so the number of non - red aces is 2.

Step3: Use the addition rule of probability

The formula for $P(A\cup R)$ is $P(A\cup R)=\frac{n(A)+n(R)-n(A\cap R)}{n(S)}$. Here, $n(A) = 4$, $n(R)=26$ and $n(A\cap R) = 2$.
So $P(A\cup R)=\frac{4 + 26- 2}{52}=\frac{28}{52}=\frac{7}{13}$.

Answer:

$\frac{7}{13}$