$\begin{array}{|c|c|c|c|} \hline &\overrightarrow{ D2} & \color{blue}{1} & \color{blue}{2} & \color{blue}{3} & \color{blue}{4} & \color{blue}{5} & \color{blue}{6} \\ \hline D1\downarrow\\\hline \color{blue}{1} &&2 &3 &4 & 5 & 6 & 7\\ \hline \color{blue}{2}&& 3 & 4&5 & 6 & 7 & 8\\ \hline \color{blue}{3} &&4 &5 &6 & 7 & 8 & \color{red}{9}\\ \hline \color{blue}{4} &&5 & 6 & 7 & 8 &\color{red}{9} &\color{red}{10}\\ \hline \color{blue}{5} &&6 &7 &8 &\color{red}{9} &\color{red}{10} &\color{red}{11} \\ \hline \color{blue}{6} && 7 & 8 & \color{red}{9} &\color{red}{10} &\color{red}{11}&\color{red}{12}\\\hline \end{array}$ Show Every cell containing a number in red, satisfies: $(D1+D2) \ge 9$ Assuming that each die is a fair die, the probability of obtaining any number from 1-6 on each of the two dice is $\frac{1}{6}$. For example, the probability of obtaining $(D1,D2)=(1,1)$ is $\left(\frac{1}{6}\right)^2 = \left(\frac{1}{36}\right)$ Every individual outcome in the table is obtained with probability $\frac{1}{36}$ as each result is equally likely. Since there are 36 (6 $\times$ 6 table) total outcomes, the probability will be $\frac{x}{36}$ or an equivalent fraction. Try to find $x$ via a simple counting method (count how many numbers in red there are).
Solution: 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.
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:
Similar QuestionsQuestion 1: What is the probability of getting a sum of 10 on two dice? Solution:
Question 2: What is the probability of getting the sum of 11? Solution:
Question 3: What is the probability of getting the sum of 12? Solution:
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