Question

A die is rolled thrice. what is the probability that the sum of the rolls is atleast 5.

Answer 1

1/6 is the probability for atleast 5

Answer 2

Number of events of getting a total of less than 5 = 4

i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1) and (2, 1, 1).

Therefore, probability of getting a total of less than 5

           P(E3) =   Number of favorable outcomes/Total number of possible outcome

P(E3) =  4/216  

P(E3) = 1/54

so, probability of getting a total of at least 5 = 1 - P (getting a total of less than 5)

= 1 - 1/54

= (54 - 1)/54

= 53/54 ANS