Problem 20 - College Algebra

Question

You are dealt one card from a standard 52-card deck. Find the probability of being dealt a card greater than 3 and less than 7 .

Step-by-Step Solution

Answer

The probability of drawing one card from a deck that is more than 3 and less than 7 is \( \frac{3}{13} \)

Step 1: Identifying the total number of favourable outcomes

Find how many cards are more than 3 and less than 7 in a standard deck. There are three for each suit (4,5,6), and four suits (hearts, diamonds, clubs, spades). Therefore, \(3 \times 4 = 12\) cards are more than 3 and less than 7 in a deck.

Step 2: Identifying the total number of possible outcomes

Calculate the total number of possible outcomes when drawing one card from a deck. A standard deck contains 52 cards, so there are 52 possible outcomes.

Step 3: Calculating the probability

Probability is calculated by dividing the number of favourable outcomes by the total number of possible outcomes. Therefore, the probability of drawing one card from a deck that is more than 3 and less than 7 is \( \frac{12}{52} = \frac{3}{13} \).