In a single throw of a pair of different dice, what is the probability of getting (i) a prime number on each dice? (ii) a total of 9 or 11?

When a pair of dice is thrown, there are 36 possible outcomes.
So, the total number of outcomes = 36
(i) The possible outcomes when both the dice has prime number on it are
(2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5).
So, the number of possible outcomes = 9
So, the probability of getting a prime number on each dice =$\frac{number of possible outcomes}{total number of outcomes}$
⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = $\frac{9}{36}$  
⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = $\frac{1}{4}$
Hence, the probability of getting a prime number on each dice is $\frac{1}{4}$ .
(ii) The possible outcomes when the sum of numbers on the dice is 9 or 11 =

$\frac{number of possible outcomes}{total number of outcomes}$
(3, 6), (4, 5), (5, 4), (5, 6), (6, 3), (6, 5).
So, the number of possible outcomes = 6
 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠  
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = $\frac{6}{36}$  
⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = $\frac{1}{6}$
Hence, the probability of getting a total of 9 or 11 is $\frac{1}{6}$