Question

two dice are thrown at the same time. Find the probability of getting : a doublet,a sum of 8,sum divisible by 5 ,sum of atleast 11

Answer 1

Number of possibilities are-
(1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6) ,
(2,1) , (2,2) , (2,3) , (2,4) , (2,5) , (2,6) ,
(3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6) ,
(4,1) , (4,2) , (4,3) , (4,4) , (4,5) , (4,6) ,
(5,1) , (5,2) , (5,3) , (5,4) , (5,5) , (5,6)
(6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,6)
total possibilities = 36

a doublet
possible number
(1,1) , (2,2) , (3,3) , (4,4) , (5,5) , (6,6)
total=6
probability=6/36= 1/6

a sum of eight
possible number
(2,6) , (3,5) , (4,4) , (5,3) , (6,2)
total=5
probability=5/36

sum divisible by 5
possible number
(1,4) , (2,3) , (3,2) , (4,1) , (4,6) , (5,5) , (7,4)
total=7
probability=7/36

sum of atleast 11
possible number
(5,6) , (6,5) , (6,6)
total=3
probability=3/36= 1/12

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I hope you Understand.... :-)

Answer 2

Sample space ={(1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6) ,(2,1) , (2,2) , (2,3) , (2,4) , (2,5) , (2,6) ,(3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6) ,(4,1) , (4,2) , (4,3) , (4,4) , (4,5) , (4,6) ,(5,1) , (5,2) , (5,3) , (5,4) , (5,5) , (5,6),(6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,6)

Total no.of outcomes=36

(i)Favourable outcomes=(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

P (a doublet)=

no.of favourable outcomes/Total no.of outcomes

=6/36

=1/6

(ii)it is in the attachment