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Concept Used: P(A) = Favorable outcomes/Total number of outcomes Calculations: Total number of possible outcomes = 6 × 6 = 36 Favorable outcomes = (1, 6) (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) ⇒ P(A) = 6/36 = 1/6 ∴ The probability of getting sum as 7 when two dice are thrown is 1/6. India’s #1 Learning Platform Start Complete Exam Preparation
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Solution: Sample space of rolling of 2 dice is as below, S = {(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)} n(S) = 36 Let A = sum of numbers is 7 = { (1, 6)(2, 5)(3, 4) (4, 3) (5, 2) (6, 1)} n(A) = 6 P (Sum of numbers is 7) = n(A) / n(S) = 6/36 = 1/6 Therefore, the probability of rolling two dice and getting a sum of 7 is 1/6. Summary: The probability of rolling two dice and getting a sum of 7 is 1/6. 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. 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.
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
Mutually exclusive events:
Not Mutually exclusive events: If the events are not mutually exclusive then
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)
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. Since, if a black ball was taken, then the probability of picking a black ball again would be 1/4, since only 2 black and 2 yellow balls would have been remaining, if a yellow ball was taken previously, the probability of taking a black ball will be 3/4. Solution:
Similar QuestionsQuestion 1: What is the probability of getting 1 on both dice? Solution:
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Question 3: What is the probability of getting the sum of 5? Solution:
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