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
(simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Determine the number of favorable outcomes

A standard deck has 52 cards. There are 4 jacks and 4 aces. Since the events of drawing a jack and drawing an ace are mutually - exclusive (a card cannot be both a jack and an ace at the same time), the number of favorable outcomes \(n\) for the event "jack or ace" is \(n = 4+4=8\).

Step2: Use the probability formula

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of elements in the event \(A\) and \(n(S)\) is the number of elements in the sample space. Here, \(n(S) = 52\) (the total number of cards in the deck) and \(n(A)=8\). So \(P=\frac{8}{52}\).

Step3: Simplify the fraction

Simplify \(\frac{8}{52}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 4. \(\frac{8\div4}{52\div4}=\frac{2}{13}\).

Answer:

\(\frac{2}{13}\)