A die is rolled two times simultaneously. Find the probability of given conditions and match the following .

Options

A. `P to (iii), Q to (ii) , R to (i)`
B. `P to (iii) , Q to (i), R to (ii)`
C. `P to (ii) , Q to (iii) , R to (i)`
D. `P to (i) , Q to (iii) , R to (ii) `

Answer

C

Explanation

Total number of outcomes = 36
P. Doublets are (1,1)(2,2),(3,3),(4,4),(5,5),(6,6).
Number of possible outcomes = 6
`therefore ` Required probability `= (6)/(36) = (1)/(6)`
Q. Even number of first die and odd number on second die `{(2,1),(2,3),(2,5),(4,1),(4,3),(4.5),(6,1),(6,3),(6,5)}`
Number of possible outcomes = 9
`therefore ` Required probability ` = (9)/(36) = (1)/(4)`
R. Sum on numbers on both die is `10:{(4,6),(6,4),(5,5)}`
Number of possible outcomes = 3
`therefore ` Required probability = `(3)/(36) = (1)/(12)`