The five letters could be arrange in 5! ways.
One of them is 'BRING'.

Correct Option: A

The five letters could be arrange in 5! ways.
One of them is 'BRING'.
∴ Required probability = 1/5!
= 1/(5 x 4 x 3 x 2 x 1)
= 1/120

Let the name of the man be A and that of his wife be B. Then ,P(A will not be alive after 10 yr and B will not be alive after 10yr) = 3/4 x 2/3 = 1/2

Correct Option: B

Let the name of the man be A and that of his wife be B. Then ,P(A will not be alive after 10 yr and B will not be alive after 10yr) = 3/4 x 2/3 = 1/2

Probability that light will be green = (Time for which light is green)/(time taken for complete cycle)

Correct Option: D

Time taken for complete cycle = 60 s
Probability that light will be green = (Time for which light is green)/(time taken for complete cycle)
= 25/60 = 5/12
∴ Probability that light will not be green = 1- 5/12 = 7/12

Let E = Event of getting same number on both the occasions
= (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

Correct Option: B

Let E = Event of getting same number on both the occasions
= (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
∴ n(E) = 6
∴ Required probability = 6/6² = 1/6

Here, n(S) = 6 x 6 = 36 and E = Event of getting a number other than 4 on any dice
= {(1, 1), (1, 2), (1, 3), (1, 5), (1, 6), (2, 1), (2, 2) , (2, 3) , (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 5), (3, 6), (5, 1) , (5, 2) , (5, 3), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 5), (6, 6) }

Correct Option: A

Here, n(S) = 6 x 6 = 36 and E = Event of getting a number other than 4 on any dice
= {(1, 1), (1, 2), (1, 3), (1, 5), (1, 6), (2, 1), (2, 2) , (2, 3) , (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 5), (3, 6), (5, 1) , (5, 2) , (5, 3), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 5), (6, 6) }
∴ P(E) = n(E) / n(S) = 25/36