In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a picture card.

Verified step by step guidance

1. Understand that a standard 52-card deck consists of 4 suits: hearts, diamonds, clubs, and spades, each with 13 cards.
2. Recognize that picture cards are the Jack, Queen, and King in each suit, totaling 3 picture cards per suit.
3. Calculate the total number of picture cards in the deck by multiplying the number of picture cards per suit (3) by the number of suits (4).
4. Subtract the total number of picture cards from the total number of cards in the deck to find the number of non-picture cards.
5. Divide the number of non-picture cards by the total number of cards in the deck to find the probability of not being dealt a picture card.

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it quantifies the chance of not being dealt a picture card from a standard deck of cards. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.

Deck of Cards

A standard deck of cards consists of 52 cards divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards, including numbered cards (2-10) and face cards (Jack, Queen, King). Understanding the composition of the deck is essential for calculating probabilities related to specific card types, such as picture cards.

Complementary Events

Complementary events are pairs of outcomes where one event occurs if and only if the other does not. In this scenario, the event of being dealt a picture card and the event of not being dealt a picture card are complementary. The probability of not being dealt a picture card can be calculated by subtracting the probability of being dealt a picture card from 1.