Question

consider the following experiment:
a card is picked at random from a standard deck of 52 cards.
what is the sample space of the experiment? what is the probability of drawing a red card from the deck if 26 of the
cards are red?
a. 26 possible outcomes; ( p(\text{red card})=\frac{1}{26} )
b. 52 possible outcomes; ( p(\text{red card})=\frac{25}{52} )
c. 52 possible outcomes; ( p(\text{red card})=\frac{1}{2} )
d. 26 possible outcomes; ( p(\text{red card})=\frac{4}{13} )

Explanation:

Step1: Determine the sample space

The sample space is the set of all possible outcomes. Since there are 52 cards in a standard deck, there are 52 possible outcomes when picking a card.

Step2: Calculate the probability of drawing a red card

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of favorable outcomes and \(n(S)\) is the number of elements in the sample space. Here, \(n(A) = 26\) (number of red cards) and \(n(S)=52\) (total number of cards). So \(P(\text{red card})=\frac{26}{52}=\frac{1}{2}\)

Answer:

C. 52 possible outcomes; \(P(\text{red card})=\frac{1}{2}\)