Solution: Show When two fair six-sided dice are rolled We have to find the probability that the sum is 9 or higher About 36 different combos are present for the two dice i.e. 6 possibilities for the first dice and 6 possibilities for the second. Among the 36, 10 have the sum 9 or higher 3 and 6 4 and 6 4 and 5 5 and 4 5 and 5 5 and 6 6 and 3 6 and 4 6 and 5 6 and 6 The favorable outcomes are {(3,6),(4,6),(4,5),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)} Number of favorable outcomes = 10 Probability = 10/36 = 5/18 Therefore, the probability that the sum is 9 or higher is 5/18. Summary: If you roll two fair six-sided dice, the probability that the sum is 9 or higher is 5/18.
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Formula Used: Probability = Possible outcomes/Total outcomes Calculations: When 2 dice are rolled, Total outcomes = 36 Possible outcomes of getting 9 = (3, 6), (6, 3), (4, 5), (5, 4) ⇒ Number of possible outcomes of getting 9 = 4 Possible outcomes of getting 10 = (4, 6), (6, 4), (5, 5) ⇒ Number of possible outcomes of getting 10 = 3 ⇒ Total number of possible outcomes = 4 + 3 = 7 Probability = Possible outcomes/Total outcomes ⇒ Probability = 7/36 ∴ The probability of getting a 9 or 10 on single throw of 2 dice is 7/36. India’s #1 Learning Platform Start Complete Exam Preparation
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Mock Tests & Quizzes Trusted by 3.3 Crore+ Students 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. 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
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. What is the probability that sum on both faces is 9 when two dice are thrown simultaneously?Solution:
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