$11$ out of $36$? I got this by writing down the number of possible outcomes ($36$) and then counting how many of the pairs had a $6$ in them: $(1,6)$, $(2,6)$, $(3,6)$, $(4,6)$, $(5,6)$, $(6,6)$, $(6,5)$, $(6,4)$, $(6,3)$, $(6,2)$, $(6,1)$. Is this correct? When two dices are rolled , there are #6xx6=36# outcomes of the type #(x,y)#, where #x# is outcome of first dice and #y# is outcome of second dice. As both #x# and #y# can take values from #1# to #6#, there are total #36# outcomes. Of these the outcomes #(1,5)#, #(2,4)#, #(3,3)#, #(4,2)# and #(5,1)# denote we have a got a sum of #6# and the outcomes #(1,6)#, #(2,5)#, #(3,4)#, #(4,3)#, #(5,2)# and #(6,1)# denote we have a got a sum of #7#. Hence there are #11# outcomes (of the total of #36# outcomes) which give us the desired output. Hence probability of getting a sum of 6 or 7 is #11/36#.
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
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
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’s the probability of rolling a sum of 6 on two dice?Solution:
Similar QuestionsQuestion 1: What is the probability of getting 6 on both dice? Solution:
Question 2: What is the probability of getting pair with 6 on only one dice? Solution:
Question 3: What is the probability of getting a pair with at-least one 6 on two dices? Solution:
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