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. jack or ace
(a) the probability that the card is a jack or an ace 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 jack or an ace, are \\( \square \\) to \\( \square \\).

Explanation:

Step1: Find the number of non - favorable outcomes

The probability of an event \(P(E)=\frac{2}{13}\). The number of favorable outcomes \(n(E)\): Let \(n(S) = 52\) (total number of cards in a deck). If \(P(E)=\frac{n(E)}{n(S)}=\frac{2}{13}\), then \(n(E)=8\) (since \(n(S) = 52\) and \(n(E)=\frac{2}{13}\times52 = 8\)). The number of non - favorable outcomes \(n(\overline{E})=n(S)-n(E)=52 - 8=44\).

Step2: Calculate the odds in favor

The formula for odds in favor of an event \(E\) is \(\text{Odds in favor}=\frac{n(E)}{n(\overline{E})}\). Substitute \(n(E) = 8\) and \(n(\overline{E})=44\) into the formula: \(\frac{8}{44}=\frac{2}{11}\).

Answer:

The odds in favor of the event of the card being a jack or an ace are \(2\) to \(11\).