Probability can be defined as a chance of occurring a particular event. The range of probabilities lies between 0 to 1, or 0% to 100% in terms of percentage. If the probability of an event is 0, the event is unlikely to happen and considered an impossible event. On the other hand, if the probability of an event is 1, it will be a certain event. In a sample space, The probabilities of all the events add up to 1. Some application of probability is in weather forecasting, 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 basic definition of probability and the formula used to find the probability. Probability basic tells how likely an event will occur. The formula for probability is,
Probability of an event = Number of favorable outcomes / Total number of outcomes
Note The probability always lies between 0 and 1.
0 ≤ P ≤ 1
For example:
Probability of getting a head on a fair two-faced coin = 1/2
As here each coin has 1 head and the total outcome is 2.
- Experiment: An observation whose result is not yet known is called an experiment.
- Random Experiment: It is an observation that is repeated a number of times and results in different outcomes. Predicting the result of a random experiment is called a probability. Drawing a card from a deck is an example of a random experiment as on each turn, you will get a different card.
- Outcome: Random experiments yield different results, known as outcomes. Suppose if we flip a coin and we get head. So, tossing a coin is a random experiment that yielded the result “head”.
- Sample space: All the possible outcomes of a random experiment constitute sample space. For example, if we roll a die, we can get 1,2,3,4,5, or 6. As a result, the sample space will have 1, 2, 3, 4, 5, and 6. This means that if a die is rolled, the sample space or the possible outcomes is 6.
- Event: When a single experiment occurs, its result is called an event. Getting a Head when tossing a coin is an example of an event. It is generally denoted by “E”.
- Possible Outcomes: All the outcomes in an experiment that is likely to occur are possible outcomes. For example, on tossing a coin, we either get head or tails, so there are 2 possible outcomes in this situation.
- Impossible Event: An event whose possibility of happening is 0 is called an impossible event. For example, getting a 17 on rolling a 6 faced-dice is impossible.
- Independent Events: Two events are said to be independent if the occurrence of one event does not affect the occurrence of the second event and vice-versa
How many Queen of Diamonds are in a deck of 52 cards?
Solution:
A deck of 52 cards consists of 4 suits: diamonds, hearts, clubs, and spades.
There are 13 cards in a suit, they are: Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.
Each suit has only one Queen card.
Therefore, In a deck of 52 cards, there is only one queen of Diamonds.
Similar Problems
Question 1: How many Jack cards are there in a deck of 52 cards?
Solution:
A deck of 52 cards consists of 4 suits: diamonds, hearts, clubs, and spades.
There are 13 cards in a suit, they are: Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.
Each suit has only one Jack card.
Total Jack cards = No of suit × No of Jack card in one Suit.
Total Jack cards = 4 × 1 = 4
Therefore, In a deck of 52 cards, there are four Jack cards.
Question 2: Find 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 52 cards consists of 4 suits: diamonds, hearts, clubs, and spades.
There are 13 cards in a suit, they are: Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.
Each suit has only one King card and there is two red suit.
Total Red King cards = No of red suit x No of King card in one Suit.
Total Red King cards = 2 × 1 = 2
Probability = 2/52 = 1/26
Therefore, In a deck of 52 cards, the probability of getting a king of the red suit is 1/26.
Question 3: Find the probability of getting a black king, if one card is picked at random from a well-shuffled deck of 52 cards.
Solution:
Total number of cards = 52
Number of black kings = 2
Total Black king cards = No of black suit × No of King card in one Suit.
Total Black King cards = 2 × 1 = 2
Probability = 2/52 = 1/26
Therefore, In a deck of 52 cards, the probability of getting a king of the black suit is 1/26.
Question 4: Find the probability of getting an ace card, if one card is picked at random from a well-shuffled deck of 52 cards.
Solution:
A deck of 52 cards consists of 4 suits: diamonds, hearts, clubs, and spades.
There are 13 cards in a suit, they are Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.
Each suit has only one ace card.
Total Ace cards = No of suit x No of Ace card in one Suit.
Total Jack cards = 4 × 1 = 4
Probability = 4/52 = 1/13
Therefore, In a deck of 52 cards, the probability of getting an Ace card is 1/13.
Question 5: Find the probability of getting a 6, if one card is picked at random from a well-shuffled deck of 52 cards.
Solution:
Each suit has only one 6 card.
Probability = 4/52 = 1/13
Therefore, In a deck of 52 cards, the probability of getting a 6 card is 1/13.