A card is drawn from a pack of 52 cards then the probability of getting a king

Solution:

Total number of cards = 52-4 = 48 [∵4 cards fell down]

So number of possible outcomes = 48

(i) Let E be the event of getting black card.

There will be 23 black cards since a black jack and 2 black kings fell down.

Number of favourable outcomes = 23

P(E) = 23/48

Hence the probability of getting black card is 23/48.

(ii) Let E be the event of getting a king.

There will be 2 kings remaining since 2 kings fell down.

Number of favourable outcomes = 2

P(E) = 2/48 = 1/24

Hence the probability of getting a king is 1/24.

(iii) Let E be the event of getting red queen.

There will be 1 red queen.

Number of favourable outcomes = 1

P(E) = 1/48

Hence the probability of queen is 1/48.

Probabilities are assigned to the outcomes of an experiment. We shall only consider experiments where all the outcomes are equally likely. Hence for drawing a card from a deck, each outcome has probability 1/52. The probability of an event is the sum of the probabilities of the outcomes in the event, hence the probability of drawing a spade is 13/52 = 1/4, and the probability of drawing a king is 4/52 = 1/13. Although the fact that the probability of getting a spade is 1/4 may make it seem that events are equally likely (since there are four suits), the probability of getting a face card is not equal to the probability of getting a number card. The only way to calculate the probability of an event is to sum the probabilities of the (equally likely) outcomes in the event. However, identifying what the equally likely outcomes are can be subtle as the following exercise illustrates.

Exercise: What are the equally likely outcomes for flipping a pair of coins? What are the equally likely outcomes for rolling a pair of dice?

Since the the probability of an event is the sum of the probabilities of the outcomes which comprise the event, one might assume that the probability of an event is the sum of the probabilities of any events which comprise that event. However, The probability of getting a black card or an ace [which we may denote as P(black or ace)] is not P(black) + P(ace) since the former is 28/52 (there are 26 black cards and 2 red aces) while the latter is 26/52 + 4/52. The discrepancy is due to the fact that the black aces are counted twice on the right hand side, once with the black cards and once with the aces. Correcting for the double counting provides the additive rule for arbitrary events: P(A or B) = P(A) + P(B) - P(A and B). Indeed 28/52 = 26/52 + 4/52 - 2/52 (there are two black aces).

Definition. Two events A and B are said to be mutually exclusive (or disjoint) if their intersection is empty (or equivalently, P(A and B) = 0). For example, the events getting a club and getting a one-eyed jack are mutually excllusive because the one-eyed jacks are the jacks of spades and hearts. The events getting a heart and getting a one-eyed jack are not mutually exclusive, because the jack of hearts is both a heart and a one eyed-jack. The additve rule for mutually exclusive events is P(A or B) = P(A) + P(B) (because P(a and B) which should be subtracted from the right hand side is equal to zero).

Definiton: A' (read A complement) is the set of outcomes which are not in A. It follows that P(A or A') = 1 and P(A and A') = 0.

Competencies:WHat is P(black or 2) What is P(Black and 2)? If you fip 3 coins, what is the probability of getting two heads? If you roll two dice, what is the probability that the sum of the pips will be 5?

Hint: Here it is a simple probability question. And we will solve this by solving the probability of getting a king out of all the cards and probability of getting a queen out of all the cards. And by adding them we will get the probability of getting a king or a queen.

Complete step-by-step answer:
The number of cards in a pack = 52
The number of the kings in a pack = 4
If we draw one card at random from the 52 cards,
Then the probability of getting a king = number of kings/number of all the cards
i.e. probability of getting a king = 4/52
Or, probability of getting a king = 1/13
The number of the queens in a pack = 4
If we draw one card at random from the 52 cards,
Then the probability of getting a queen = number of queens/number of all the cards
i.e. probability of getting a queen = 4/52
Or, probability of getting a queen = 1/13
The probability of getting a king or a queen out of all the cards = probability of getting a king out of all the cards + probability of getting a queen out of all the cards
= 1/13 + 1/13
= (1+1)/13
= 2/13
Hence the probability of getting a king or a queen out of 52 cards is 2/13.

Note: You might mistake the question as a king and a queen in place of a king or a queen.
Probability is concerned with numerical description of how likely an event is to occur and how likely it is that a proposition is true. It is always between 0 and 1.
The formula of probability in simple language is, number of favorable outcomes/total outcomes.
You should practice similar questions of probability related to cards, dice, coins, balls etc.

What is the probability of getting a king in a pack of 52 cards?

How many kings are in 52 cards?

Is drawn from a pack of 52 cards find the probability of getting a king or a heart or a red card?

What is a probability that if a card is drawn from 52 pack of cards it is a diamond?