Question

for the experiment of drawing a single card from a standard 52 - card deck, find (a) the probability of the following event, and (b) the odds in favor of the followin spade or face card (a) the probability that the card is either a spade or a face card is \\( \frac { 11 } { 26 } \\) (simplify your answer.) (b) the odds, in simplified form, in favor of the event of the card being a spade or a face card, are \\( \square \\) to \\( \square \\).

Explanation:

Step1: Recall the formula for odds

The formula for odds in favor of an event \(E\) is \(\text{Odds}=\frac{P(E)}{1 - P(E)}\), where \(P(E)\) is the probability of the event \(E\).

Step2: Substitute the given probability

We are given \(P(E)=\frac{11}{26}\). Then \(1 - P(E)=1-\frac{11}{26}=\frac{26 - 11}{26}=\frac{15}{26}\).

Step3: Calculate the odds

\(\text{Odds}=\frac{\frac{11}{26}}{\frac{15}{26}}\). When dividing by a fraction, we multiply by its reciprocal: \(\frac{11}{26}\times\frac{26}{15}=\frac{11}{15}\)

Answer:

The odds in favor of the event are \(11\) to \(15\)