Textbook Question
The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of no flooding for four consecutive years?
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10. Combinatorics & Probability
Probability
2:30 minutesProblem 91
Textbook Question
You are dealt one card from a 52-card deck. Find the probability of getting an ace or a king.
Verified step by step guidance1
Step 1: Understand the problem. You are tasked with finding the probability of drawing either an ace or a king from a standard 52-card deck. A standard deck has 52 cards divided into 4 suits (hearts, diamonds, clubs, spades), with each suit containing 13 cards.
Step 2: Determine the total number of favorable outcomes. There are 4 aces (one in each suit) and 4 kings (one in each suit) in the deck. Since these events are mutually exclusive (an ace cannot also be a king), the total number of favorable outcomes is 4 (aces) + 4 (kings) = 8.
Step 3: Calculate the total number of possible outcomes. The total number of cards in the deck is 52, so there are 52 possible outcomes when drawing one card.
Step 4: Use the probability formula. The probability of an event is given by the formula: . Substitute the values: favorable outcomes = 8 and total outcomes = 52.
Step 5: Simplify the fraction to express the probability in its simplest form. Divide the numerator and denominator by their greatest common divisor (GCD), if applicable.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 drawing a specific type of card from a deck. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.
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Favorable Outcomes
Favorable outcomes refer to the specific results that satisfy the conditions of the event we are interested in. In this case, the favorable outcomes are the aces and kings in a standard 52-card deck. There are 4 aces and 4 kings, making a total of 8 favorable outcomes for this probability problem.
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Total Outcomes
Total outcomes represent the complete set of possible results in a probability scenario. For a standard deck of cards, there are 52 total outcomes since there are 52 cards. Understanding the total number of outcomes is crucial for calculating the probability of drawing an ace or a king.
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