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What is the probability of getting a king or a queen in a single draw from a pack of 52 cards?

  • Last Updated : 22 Sep, 2021

Probability is a field of mathematics that studies the likelihood of a random event occurring. Since many events cannot be predicted with total certainty, we use probability to anticipate how probable they are to occur. Probability can range from 0 to 1, with 0 indicating an improbable event and 1 indicating a certain event. Probability has many applications. Risk assessment and modeling are examples of how probability theory is used in everyday life. Actuarial science is used by the insurance sector and markets to establish pricing and make trading decisions. Environmental control, entitlement analysis, and financial regulation all use probability methodologies. Probability also finds its applications in weather forecasting, agriculture, and politics.

Formula for Probability

Probability of an event, P(A) = (Number of favorable outcomes) / (Total number of outcomes)  

Types of Probability

There are majorly three types of probability, they are theoretical probability, experimental probability, and axiomatic probability. Let’s learn about them in detail,

Theoretical Probability

It is predicated on the likelihood of something occurring. The rationale behind probability is the foundation of theoretical probability. For example, to calculate the theoretical probability of rolling a die and getting the number 3, we must first know the number of possible outcomes. We know that a die has six numbers (i.e. 1, 2, 3, 4, 5, 6), hence the number of possible outcomes is six as well. So, the probability of rolling a three on a dice is one in six, or 1/6

Experimental Probability

Experimental probability, unlike theoretical probability, incorporates the number of trials, i.e. it is based on the results of an experiment. The experimental probability can be computed by dividing the total number of trials by the number of possible outcomes. For example, if a dice is rolled 40 times and the number three is recorded 10 times then, the experimental probability for heads is 10/40 or 1/4

Axiomatic Probability

A set of principles or axioms are established in the axiomatic probability that applies to all types. Kolmogorov established these axioms, which are known as Kolmogorov’s three axioms. There are three main concepts in probability. They are sample space, events, and probability function. Let’s learn about them in detail,

Sample Space (S)

A sample space is the collection of all possible outcomes of an experiment. Tossing three dice produces a sample space of 216 potential outcomes, each of which may be recognized by an ordered set (a, b, c), where a, b, and c take one of the following values: 1, 2, 3, 4, 5, 6.

Event (A)

A well-defined subset of the sample space is referred to as an event. The event the sum of the faces shown on the two dice equals five has six outcomes: (1, 1, 3), (1, 3, 1), (3, 1, 1), (1, 2, 2), (2, 2, 1) and (2, 1, 1).

Probability Function (P)

The function that is used to assign a probability to an occurrence is known as the Probability Function (P). The probability function (P) determines the likelihood of an event (A) being drawn from the sample space (S).

What is the probability of getting a king or a queen in a single draw from a pack of 52 cards?

Solution:

Total number of cards in a deck = 52

Total number of kings in a deck of 52 cards = 4

If we pick one card at random from the 52 cards, the probability of getting a king = Total number of kings in the deck / Total number of cards in the deck.

i.e. Probability of getting a king = 4/52 = 1/13

Total number of queens in a deck of 52 cards = 4

If we pick one card at random from the 52 cards, the probability of getting a queen = Total number of queens in the deck / Total number of cards in the deck.

i.e. Probability of getting a queen = 4/52= 1/13

Therefore, probability of getting a king or a queen, P(E) = probability of getting a king + probability of getting a queen = 1/13 + 1/13 = 2/13

Similar Questions

Question 1:  Find the probability of getting a red king.

Solution:

Total number of cards = 52

No. of favorable cards that are red kings = 2

Therefore probability of getting a red king = 2/52 = 1/26

Question 2: Find the probability of getting a red non-face card.

Solution:

Total number of red cards in a deck = 26

Face cards are cards that are either, king, queen, or jack

Total number of red face cards = 6

Therefore, the total number of red non-face cards = 26 – 6

Therefore, the probability of getting a red non-face card= 20/52 = 5/13

Question 3: Find the probability of getting a black card.

Solution:

Total number of cards = 52

Total number of suits = 4

Total number of black suits = 2

Therefore, total number of black cards = 2 × 13 = 26

Therefore the probability of getting a black card= Total number of black cards in the deck / total number of cards in the deck = 26/52 = 1/2.

Question 4: Find the probability of getting a red ace or a spade.

Solution:

Total number of cards = 52

No. of favorable cards that are red aces = 2

Therefore the probability of getting a red ace = 2/52

Total number of cards that are spades =13

Therefore the probability of getting a spade = 13/52

Therefore, probability of getting a red ace or a spade, P(E) = probability of getting a red ace + probability of getting a spade = 2/52 + 13/52 = 15/52

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