You are playing with an ordinary deck of 52 cards by drawing...

You are playing with an ordinary deck of 52 cards by drawing cards at random and looking at them. a) Find the probability that the card you draw is (i) the ace of hearts (ii) the ace of hearts or any spade (iii) an ace or any heart (iv) not a face card. b) Now you draw the ten of diamonds, put it on the table and draw a second card. What is the probability that the second card is (i) the ace of hearts? (ii) not a face card? c) Now you draw the ten of diamonds, return it to the deck and draw a second card. What is the probability that the second card is (i) the ace of hearts? (ii) not a face card?

You are playing with an ordinary deck of 52 cards by drawing cards at random and looking at them.
a) Find the probability that the card you draw is
(i) the ace of hearts
(ii) the ace of hearts or any spade
(iii) an ace or any heart
(iv) not a face card.
b) Now you draw the ten of diamonds, put it on the table and draw a second card. What is the probability that the second card is
(i) the ace of hearts?
(ii) not a face card?
c) Now you draw the ten of diamonds, return it to the deck and draw a second card. What is the probability that the second card is
(i) the ace of hearts?
(ii) not a face card?

Key Concepts

Basic Probability

This concept involves determining the likelihood of events by comparing the number of favorable outcomes to the total number of outcomes. It is fundamental to solving problems in probability, including those involving card draws from a deck.

Counting Principles in a Deck of Cards

A standard deck contains 52 uniquely defined cards, divided into suits and ranks. Understanding how to count cards with specific properties, such as identifying a particular card, a suit, or a category like face cards, is crucial for calculating probabilities in card problems.

Addition Rule for Probabilities

This rule is used to find the probability of the occurrence of at least one of multiple events. It requires summing the probabilities of the separate events, with adjustments made for any overlap when the events are not mutually exclusive.

Conditional Probability and Effects of Without Replacement

When drawing cards without replacement, the outcome of the first draw influences the composition of the deck for the subsequent draw. This change in the sample space must be accounted for when determining the probability of events in sequential draws.

Replacement in Probability

In scenarios where a card is returned to the deck before drawing again, the draws are independent. This means the probabilities remain constant from one draw to the next, as the deck is restored to its full state.

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