type the correct answer in the box. if necessary, use / for the fraction bar. give your answer in reduced…

type the correct answer in the box. if necessary, use / for the fraction bar. give your answer in reduced form.\na 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 \nreset next

type the correct answer in the box. if necessary, use / for the fraction bar. give your answer in reduced form.\na 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 \nreset next

Answer

Explanation:

Step1: Determine total number of cards

A standard deck has 52 cards, so $n(S)=52$.

Step2: Find number of aces

There are 4 aces in a deck, so $n(A) = 4$.

Step3: Find number of red cards

There are 26 red cards in a deck, so $n(R)=26$.

Step4: Find number of red - aces

There are 2 red - aces, so $n(A\cap R)=2$.

Step5: Use the addition rule of probability

The formula for $P(A\cup R)$ is $P(A\cup R)=\frac{n(A)+n(R)-n(A\cap R)}{n(S)}$. Substitute the values: $\frac{4 + 26-2}{52}=\frac{28}{52}=\frac{7}{13}$.

Answer:

$\frac{7}{13}$