Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty. The higher or lesser the probability of an event, the more likely it is that the event will occur or not respectively. Show For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2. So, the probability of an event is Favorable outcomes/Total number of outcomes. It is denoted with the parenthesis i.e. P(Event).
What is Sample Space? All the possible outcomes of an event are called Sample spaces. Examples-
Types of EventsIndependent Events: If two events (A and B) are independent then their probability will be Example: If two coins are flipped, then the chance of both being tails is 1/2 * 1/2 = 1/4 Mutually exclusive events:
Example – The chance of rolling a 2 or 3 on a six-faced die is P (2 or 3) = P (2) + P (3) = 1/6 + 1/6 = 1/3 Not Mutually exclusive events: If the events are not mutually exclusive then P (A or B) = P (A ∪ B) = P (A) + P (B) − P (A and B) What is Conditional Probability? For the probability of some event A, the occurrence of some other event B is given. It is written as P (A ∣ B) P (A ∣ B) = P (A ∩ B) / P (B) Example- In a bag of 3 black balls and 2 yellow balls (5 balls in total), the probability of taking a black ball is 3/5, and to take a second ball, the probability of it being either a black ball or a yellow ball depends on the previously taken out ball. Some points related to Cards:
Find the probability of getting a Queen from a well-shuffled deck of 52 cards.Solution:
Similar QuestionsQuestion 1: When a single card is drawn from a well-shuffled 52 card deck, then find the probability of getting a king? Solution:
Question 2: When a single card is drawn from a well-shuffled 52 card deck find the probability of getting a red queen? Solution:
Question 3: When a single card is drawn from a well-shuffled 52 card deck find the probability of getting a black queen? Solution:
Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that at the card drawn is neither a red card nor a queen. n(S) = 52. Event = {getting neither a red card nor a queen} Number of cards each one of which is either a red card or a queen = 28. The event that the card drawn is neither a red card nor a queen = 52 - 28 = 24. n(E) = 24n(S) = 52 P(E) = ? ∴ P(E) = `"n(E)"/"n(S)" = 24/52 = 6/13.` Concept: Random Experiments Is there an error in this question or solution? |