Solution: Show We use the basic formula of probability to solve the problem. Probability = Number of possible outcomes/Total number of favorable outcomes. Total number of cards from a well-shuffled deck = 52 Number of spade cards = 13 Number of heart cards = 13 Number of diamond cards = 13 Number of club cards = 13 Total number of kings = 4 Total number of queens = 4 Total number of jacks = 4 Number of face cards = 12 (i) Probability of getting a king of red colour = Number of red colour king/Total number of outcomes We will have 2 red kings (Heart and Diamond) = 2/52 = 1/26 (ii) Probability of getting a face card = Number of face cards/Total number of outcomes 12/52 = 3/13 (iii) Probability of getting a red face card = Number of red face cards/Total number of outcomes We will have 3 diamond face cards and 3 heart face cards that sum up to 6 red face cards. = 6/52 = 3/26 (iv) Probability of getting the jack of hearts = Number of jack of hearts/Total number of outcomes = 1/52 (v) Probability of getting a spade card = Number of spade cards/Total number of outcomes = 13/52 = 1/4 (vi) Probability of getting the queen of diamonds = Number of possible outcomes/Total number of favourable outcomes = 1/52 Check out more in terms of probability. ☛ Check: NCERT Solutions for Class 10 Maths Chapter 15 Video Solution: NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 Question 14 Summary: If one card is drawn from a well-shuffled deck of 52 cards, then the probability of getting (i) a king of red colour, (ii) a face card, (iii) a red face card, (iv) the jack of hearts, (v) a spade, and (vi) the queen of diamonds are 1/26, 3/13, 3/26, 1/52, 1/4, and 1/52 respectively. ☛ Related Questions:
Learning Outcomes
Probability is the likelihood of a particular outcome or event happening. Statisticians and actuaries use probability to make predictions about events. An actuary that works for a car insurance company would, for example, be interested in how likely a 17 year old male would be to get in a car accident. They would use data from past events to make predictions about future events using the characteristics of probabilities, then use this information to calculate an insurance rate. In this section, we will explore the definition of an event, and learn how to calculate the probability of it’s occurance. We will also practice using standard mathematical notation to calculate and describe different kinds of probabilities.  Basic ConceptsIf you roll a die, pick a card from deck of playing cards, or randomly select a person and observe their hair color, we are executing an experiment or procedure. In probability, we look at the likelihood of different outcomes. We begin with some terminology. Events and Outcomes
If we roll a standard 6-sided die, describe the sample space and some simple events.
Given that all outcomes are equally likely, we can compute the probability of an event E using this formula: [latex]P(E)=\frac{\text{Number of outcomes corresponding to the event E}}{\text{Total number of equally-likely outcomes}}[/latex]
If we roll a 6-sided die, calculate
This video describes this example and the previous one in detail. Let’s say you have a bag with 20 cherries, 14 sweet and 6 sour. If you pick a cherry at random, what is the probability that it will be sweet?
At some random moment, you look at your clock and note the minutes reading. a. What is probability the minutes reading is 15? b. What is the probability the minutes reading is 15 or less?
A standard deck of 52 playing cards consists of four suits (hearts, spades, diamonds and clubs). Spades and clubs are black while hearts and diamonds are red. Each suit contains 13 cards, each of a different rank: an Ace (which in many games functions as both a low card and a high card), cards numbered 2 through 10, a Jack, a Queen and a King.
Compute the probability of randomly drawing one card from a deck and getting an Ace. This video demonstrates both this example and the previous cherry example on the page. Certain and Impossible events
In the course of this section, if you compute a probability and get an answer that is negative or greater than 1, you have made a mistake and should check your work. Types of EventsComplementary EventsNow let us examine the probability that an event does not happen. As in the previous section, consider the situation of rolling a six-sided die and first compute the probability of rolling a six: the answer is P(six) =1/6. Now consider the probability that we do not roll a six: there are 5 outcomes that are not a six, so the answer is P(not a six) = [latex]\frac{5}{6}[/latex]. Notice that [latex]P(\text{six})+P(\text{not a six})=\frac{1}{6}+\frac{5}{6}=\frac{6}{6}=1[/latex] This is not a coincidence. Consider a generic situation with n possible outcomes and an event E that corresponds to m of these outcomes. Then the remaining n – m outcomes correspond to E not happening, thus [latex]P(\text{not}E)=\frac{n-m}{n}=\frac{n}{n}-\frac{m}{n}=1-\frac{m}{n}=1-P(E)[/latex]
The complement of an event is the event “E doesn’t happen”
If you pull a random card from a deck of playing cards, what is the probability it is not a heart? This situation is explained in the following video. Probability of two independent events
Suppose we flipped a coin and rolled a die, and wanted to know the probability of getting a head on the coin and a 6 on the die. The prior example contained two independent events. Getting a certain outcome from rolling a die had no influence on the outcome from flipping the coin.
Events A and B are independent events if the probability of Event B occurring is the same whether or not Event A occurs.
Are these events independent?
When two events are independent, the probability of both occurring is the product of the probabilities of the individual events.
If events A and B are independent, then the probability of both A and B occurring is [latex]P\left(A\text{ and }B\right)=P\left(A\right)\cdot{P}\left(B\right)[/latex] where P(A and B) is the probability of events A and B both occurring, P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring If you look back at the coin and die example from earlier, you can see how the number of outcomes of the first event multiplied by the number of outcomes in the second event multiplied to equal the total number of possible outcomes in the combined event.
In your drawer you have 10 pairs of socks, 6 of which are white, and 7 tee shirts, 3 of which are white. If you randomly reach in and pull out a pair of socks and a tee shirt, what is the probability both are white? Examples of joint probabilities are discussed in this video. The previous examples looked at the probability of both events occurring. Now we will look at the probability of either event occurring.
Suppose we flipped a coin and rolled a die, and wanted to know the probability of getting a head on the coin or a 6 on the die.
The probability of either A or B occurring (or both) is [latex]P(A\text{ or }B)=P(A)+P(B)–P(A\text{ and }B)[/latex]
Suppose we draw one card from a standard deck. What is the probability that we get a Queen or a King? See more about this example and the previous one in the following video. In the last example, the events were mutually exclusive, so P(A or B) = P(A) + P(B).
Suppose we draw one card from a standard deck. What is the probability that we get a red card or a King?
In your drawer you have 10 pairs of socks, 6 of which are white, and 7 tee shirts, 3 of which are white. If you reach in and randomly grab a pair of socks and a tee shirt, what the probability at least one is white?
The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their car. Find the probability that a randomly chosen person:
This table example is detailed in the following explanatory video. Conditional ProbabilityIn the previous section we computed the probabilities of events that were independent of each other. We saw that getting a certain outcome from rolling a die had no influence on the outcome from flipping a coin, even though we were computing a probability based on doing them at the same time. In this section, we will consider events that are dependent on each other, called conditional probabilities.
The probability the event B occurs, given that event A has happened, is represented as P(B | A) This is read as “the probability of B given A” For example, if you draw a card from a deck, then the sample space for the next card drawn has changed, because you are now working with a deck of 51 cards. In the following example we will show you how the computations for events like this are different from the computations we did in the last section.
What is the probability that two cards drawn at random from a deck of playing cards will both be aces?
If Events A and B are not independent, then P(A and B) = P(A) · P(B | A)
If you pull 2 cards out of a deck, what is the probability that both are spades?
The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their car. Find the probability that a randomly chosen person:
These kinds of conditional probabilities are what insurance companies use to determine your insurance rates. They look at the conditional probability of you having accident, given your age, your car, your car color, your driving history, etc., and price your policy based on that likelihood. View more about conditional probability in the following video.
If you draw two cards from a deck, what is the probability that you will get the Ace of Diamonds and a black card? These two playing card scenarios are discussed further in the following video.
A home pregnancy test was given to women, then pregnancy was verified through blood tests. The following table shows the home pregnancy test results. Find
See more about this example here. |
When a card is selected at random from a 52 card deck What is the probability that the card is a face card king Queen Jack or a spade?
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