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
Is Ace a face card or a numbered 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.
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.