Question

for the experiment of drawing a single card from a standard 52 - card deck, find (a) the probability of the event below, and (b) the odds in favor of the given event. king or queen (a) the probability that the card is a king or a queen is $\frac{2}{13}$. (simplify your answer. type an integer or a fraction.) (b) the odds, in simplified form, in favor of the event of the card being a king or a queen, are $square$ to $square$.

Explanation:

Step1: Calculate number of favorable outcomes

A standard deck has 4 kings and 4 queens. So, number of favorable outcomes $n = 4 + 4=8$.

Step2: Recall total number of outcomes

Total number of cards in a deck is $N = 52$.

Step3: Calculate probability (already given but for context)

Probability $P=\frac{n}{N}=\frac{8}{52}=\frac{2}{13}$.

Step4: Calculate odds

Odds in favor of an event $E$ is given by $\frac{P(E)}{1 - P(E)}$. Since $P(E)=\frac{2}{13}$, then $1 - P(E)=1-\frac{2}{13}=\frac{11}{13}$. So, odds in favor $=\frac{\frac{2}{13}}{\frac{11}{13}}=\frac{2}{11}$, which means 2 to 11.

Answer:

(a) $\frac{2}{13}$
(b) 2 to 11