Q => A die is thrown twice. What is the probability that(i) 5 will not

1.	Q => A die is thrown twice. What is the probability that(i) 5 will not come up either time? (ii) 5 will come up at least once?
Answer» $\huge\star\:\:{\orange{\underline{\purple{\mathbf{Question}}}}}$ A dice is THROWN twice. What is the probability that (i) 5 will not come up either time ? (II) 5 will come up at LEAST once ? $\huge\star\:\:{\orange{\underline{\red{\mathbf{Answer}}}}}$ Probability of getting 5 on throwing the dice once . Sample space $\begin{cases}(5,1)\\(5,2)\\(5,3)\\(5,4)\\(5,5)\\(5,6)\end{cases}$ For tossing it twice we have 11 outcomes Number of outcomes we get on throwing a dice once = 18 So , hence total outcomes on throwing it twice = 18 × 2 = 36 Number of times we can get a 5 = 11 i ) Number of times we won't get a 5 $\hookrightarrow\:36\:-\:11\:=\:25$ Event 1 = Probability of not getting a 5 either time Event 1 = $\frac{Favorable\: outcomes}{Total\: number\:of\: outcomes}$ Event 1 = $\dfrac{25}{36}$ _____________________________________ ii ) Number of times we will get 5 atleast once = 11 Event 2 = Probability of getting a 5 atleast one time Event 2 = $\frac{Favorable\: outcomes}{Total\: number\:of\: outcomes}$ Event 2 = $\dfrac{11}{36}$ _______________________________________