What is the probability of getting jack or ace from a well shuffled pack of 52 cards 1 marks?

Return to Statistics Topics

Summary of Basic Probability

The classical or theoretical definition of probability assumes that there are a finite number of outcomes in a situation and all the outcomes are equally likely.

Classical Definition of Probability

Though you probably have not seen this definition before, you probably have an inherent grasp of the concept. In other words, you could guess the probabilities without knowing the definition.

Cards and Dice The examples that follow require some knowledge of cards and dice. Here are the basic facts needed compute probabilities concerning cards and dice.

A standard deck of cards has four suites: hearts, clubs, spades, diamonds. Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king. Thus the entire deck has 52 cards total.

When you are asked about the probability of choosing a certain card from a deck of cards, you assume that the cards have been well-shuffled, and that each card in the deck is visible, though face down, so you do not know what the suite or value of the card is.

A pair of dice consists of two cubes with dots on each side. One of the cubes is called a die, and each die has six sides.Each side of a die has a number of dots (1, 2, 3, 4, 5 or 6), and each number of dots appears only once.

Example 1 The probability of choosing a heart from a deck of cards is given by

Example 2 The probability of choosing a three from a deck of cards is

Example 3 The probability of a two coming up after rolling a die (singular for dice) is

The classical definition works well in determining probabilities for games of chance like poker or roulette, because the stated assumptions readily apply in these cases. Unfortunately, if you wanted to find the probability of something like rain tomorrow or of a licensed driver in Louisiana being involved in an auto accident this year, the classical definition does not apply. Fortunately, there is another definition of probability to apply in these cases.

Empirical Definition of Probability

The probability of event A is the number approached by

as the total number of recorded outcomes becomes "very large."

The idea that the fraction in the previous definition will approach a certain number as the total number of recorded outcomes becomes very large is called the Law of Large Numbers. Because of this law, when the Classical Definition applies to an event A, the probabilities found by either definition should be the same. In other words, if you keep rolling a die, the ratio of the total number of twos to the total number of rolls should approach one-sixth. Similarly, if you draw a card, record its number, return the card, shuffle the deck, and repeat the process; as the number of repetitions increases, the total number of threes over the total number of repetitions should approach 1/13 ≈ 0.0769.

In working with the empirical definition, most of the time you have to settle for an estimate of the probability involved. This estimate is thus called an empirical estimate.

Example 4 To estimate the probability of a licensed driver in Louisiana being involved in an auto accident this year, you could use the ratio

To do better than that, you could use the number of accidents for the last five years and the total number of Louisiana drivers in the last five years. Or to do even better, use the numbers for the last ten years or, better yet, the last twenty years.

Example 5 Estimating the probability of rain tomorrow would be a little more difficult. You could note today's temperature, barometric pressure, prevailing wind direction, and whether or not there are rain clouds that could be blown into your area by tomorrow. Then you could find all days on record in the past with similar temperatures, pressures, and wind directions, and clouds in the right location. Your rainfall estimate would then be the ratio

To make your estimate better, you might want to add in humidity, wind speed, or season of the year. Or maybe if there seemed to be no relation between humidity levels and rainfall, you might want add in the days that did not meet your humidity level requirements and thus increase the total number of days.

Example 6 If you want to estimate the probability that a dam will burst, or a bridge will collapse, or a skyscraper will topple, there is usually not much past data available. The next best thing is to do a computer simulation. Simulation results can be compiled a lot faster with a lot less money and less loss of life than actual events. The estimated probability of say a bridge collapsing would be given by the following fraction

The more true to life the simulation is, the better the estimate will be.

Basic Probability Rules For either definition, the probability of an event A is always a number between zero and one, inclusive; i.e.

Sometimes probability values are written using percentages, in which case the rule just given is written as follows

If the event A is not possible, then P(A) = 0 or P(A) = 0%. If event A is certain to occur, then P(A) = 1 or P(A) = 100%.

The sum of the probabilities for each possible outcome of an experiment is 1 or 100%. This is written mathematically as follows using the capital Greek letter sigma (S) to denote summation.

Probability Scale* The best way to find out what the probability of an event means is to compute the probability of a number of events you are familiar with and consider how the probabilities you compute correspond to how frequently the events occur. Until you have computed a large number of probabilities and developed your own sense of what probabilities mean, you can use the following probability scale as a rough starting point. When you gain more experience with probabilities, you may want to change some terminology or move the boundaries of the different regions.

*This is a revised and expanded version of the probability scale presented in Mario Triola, Elementary Statistics Using the Graphing Calculator: For the TI-83/84 Plus, Pearson Education, Inc. 2005, page 135.

Return to Statistics Topics

Improve Article

Save Article

Probability can be defined as a chance of happening a particular event. The range of chances lies between 0 to 1, or 0 to 100 in terms of percentage. However, the event is doubtful to occur and called an impossible event, if the probability of an event is 0. On the other hand, if the probability of an event is 1, it will be a certain event. In a sample space, the chances of all the events add up to 1. Some use of probability is in rainfall prediction, flipping a coin, rolling dice, in sports and board games.

Important terms related to probability

Before learning about the terms used in probability. Let’s first take a look at the fundamental description of probability and the formula used to find the probability. Probability basically tells how likely an event will happen. The formula for probability is,

Probability of an event = Number of favorable results/ Total number of results

Note: The probability unfailingly lies between 0 and 1.

0 ≤ P ≤ 1

For instance, the Probability of picking up a head on a fair two-faced coin = 1/2. As of right now, each coin has 1 head and the total favorable outcome is 2.  

• Experiment: An observation whose consequence isn’t eventually known, is called an experiment.
• Random Experiment: It’s an observation that’s reiterated a number of times and concludes in different consequences. Predicting the result of an arbitrary trial is known as probability. Picking a card from a deck is an instance of a random experiment as on each turn, one would pick up a distinct card.
• Outcome: Random trials yield distinct results, known as outcomes. On flipping a coin, suppose head is obtained. So, tossing a coin is a random experiment that gave in the result “head”.
• Sample space: All the achievable outcomes of random experimentation make up sample space. For illustration, if a dice is rolled, pick up 0 or 6. In conclusion, the sample space will have numbers 1 through 6. This means that if a dice is rolled, the sample space or the possible outcomes is 6.
• Event: When a single trial occurs, its conclusion is called an event. picking up a Head when tossing a coin is an instance of an event. It’s generally expressed by “E”.
• Possible Outcomes: All the results in experimentation that are probable to happen are possible outcomes. For case, on tossing a coin, either pick up heads or tails, thus there are 2 feasible results in this situation.
• Impossible Event: An event whose possibility of occurring is 0 is called an impossible event. For instance, getting a 17 on rolling a 6 faced- die is impossible.
• Independent Events: Two events are said to be independent if the happening of one event doesn’t affect the happening of the other event and vice-versa

Solution: 

A deck of cards contains 52 cards which has 4 suits: diamonds, hearts, clubs, and spades.

Each suit of a deck has 13 cards namely, Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.

Each suit has only three face cards: King, Queen, and Jack.

Therefore, Ace card is a numbered card.

Similar Problems

Question 1: Find the number of Jack cards in a deck of 52 cards?

Solution:

A deck of cards contains 52 cards which has 4 suits: diamonds, hearts, clubs, and spades.

Each suit of a deck has 13 cards namely, Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.

Each suit has only three face cards: King, Queen, and Jack.

Each suit has only one Jack card.

Total Jack cards will be No of suit times No of Jack card in one Suit.

Total Jack cards is equal to 4 × 1 that is 4.

Therefore, there are four Jack cards in a deck of 52 cards.

Question 2: What will be the probability of getting a red king, if one card is picked at random from a well-shuffled deck of 52 cards.

Solution:

A deck of cards contains 52 cards which has 4 suits: diamonds, hearts, clubs, and spades.

Each suit of a deck has 13 cards namely, Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.

Each suit has only three face cards: King, Queen, and Jack.

There are two red suit and each of the suit has only one King card.

Total Red King cards is equal to No of red suit times No of King card in one Suit.

Total Red King cards will be 2 × 1 that is 2

Probability = 2/52 = 1/26

Therefore, the probability of getting a king of the red suit is 1/26 in a deck of 52 cards.

Question 3: If one card is picked at random from a well-shuffled deck of 52 cards, find the probability of getting a black king.

Solution:

Total number of cards = 52

Number of black kings = 2

Total Black king cards is equal to No of black suit times No of King card in one Suit.

Total Black King cards will be 2 × 1 that is 2

Probability = 2/52 = 1/26

Therefore, the probability of getting a king of the black suit is 1/26 in a deck of 52 cards.

Question 4: If one card is picked at random from a well-shuffled deck of 52 cards, find the probability of getting an ace card.

Solution:

A deck of cards contains 52 cards which has 4 suits: diamonds, hearts, clubs, and spades.

Each suit of a deck has 13 cards namely, Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.

Each suit has only three face cards: King, Queen, and Jack.

Each suit has only one ace card.

Total Ace cards will be No of suit times No of Ace card in one Suit.

Total Jack cards = 4 × 1 = 4

Probability = 4/52 = 1/13

Therefore, the probability of getting an Ace card is 1/13 in a deck of 52 cards.

Question 5: If one card is picked at random from a well-shuffled deck of 52 cards, Find the probability of getting a 6.

Solution:

Each suit has only one 6 card.

Probability = 4/52 = 1/13

Therefore, the probability of getting a 6 card is 1/13 In a deck of 52 cards.