Total number of marbles = 6 + 4 + 2 + 3 = 15
Ways of selection of two red marbles = n(E) = ⁶C₂
Ways of selection of two marbles = n(S) = ¹⁵C₂

Correct Option: D

Total number of marbles = 6 + 4 + 2 + 3 = 15
Ways of selection of two red marbles = n(E) = ⁶C₂
Ways of selection of two marbles = n(S) = ¹⁵C₂
So, required probability = (⁶C₂) / (¹⁵C₂)
= (6 x 5) / (15 x 14) = 1/7

Number of ways to select 3 marbles out of 7 marbles = n(s) = ⁷C₃ = 35
Probability that 2 are green and 1 is red = n(E) = ⁴C₂ x ³C₁ = 18

Correct Option: B

Number of ways to select 3 marbles out of 7 marbles = n(s) = ⁷C₃ = 35
Probability that 2 are green and 1 is red = n(E) = ⁴C₂ x ³C₁ = 18
∴ Required probability = 18/35

Required probability = (²C₁ x ³C₂ + ²C₂ x ³C₁) / (⁵C₃)

Correct Option: C

Required probability = (²C₁ x ³C₂ + ²C₂ x ³C₁) / (⁵C₃) = 9/10

n(s) = 50
Prime numbers are = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
∴ n(E) = 15

Correct Option: C

n(s) = 50
Prime numbers are = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
∴ n(E) = 15
∴ p(E) = 15/50 = 3/10 = 0.3

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