Question

an ordinary deck of playing cards has 52 cards. there are four suits - spades, hearts, diamonds, and clubs - with 13 cards in each suit. spades and clubs are black; hearts and diamonds are red. one of these cards is selected at random. let a denote the event that a 10 is chosen. find the probability that a 10 is chosen, and express your answer in probability notation. the probability that a 10 is chosen is p(a) = (type an integer or a decimal. round to three decimal places as needed.)

Explanation:

Step1: Determine the number of favorable outcomes

There are 4 tens in a deck (one for each suit). So the number of favorable outcomes \( n(A)=4 \).

Step2: Determine the total number of outcomes

The total number of cards in the deck is \( N = 52 \).

Step3: Calculate the probability

The probability formula is \( P(A)=\frac{n(A)}{N} \). Substituting the values, we get \( P(A)=\frac{4}{52}=\frac{1}{13}\approx0.077 \).

Answer:

\( P(A) = 0.077 \)