Total ways = ¹³c₂
Favourable number ways of selecting men only = ⁸c₂
∴ Probability of selecting no woman
= ⁸c₂ / ¹³c₂
= 14/39

Correct Option: A

Total ways = ¹³c₂
Favourable number ways of selecting men only = ⁸c₂
∴ Probability of selecting no woman
= ⁸c₂ / ¹³c₂
= 14/39
∴ Probability of selecting at least one woman
= 1 - (14 / 39)
= 25 / 39

Total events = n (s) = 2⁵ = 32
n(E) of getting heads = 1
p(E) = 1/32
∴ n(E) = 1 - p(E)

Correct Option: A

Total events = n (s) = 2⁵ = 32
n(E) of getting heads = 1
p(E) = 1/32
∴ n(E) = 1 - p(E) = 1 - 1/32 = 31/32

Let P(B) = x
Given, P(A∪B) = 0.8 and P(A) = 0.3
⇒ P(A) + P(B) - P(A∩B) = 0.8
⇒ P(A) + P(B) - P(A) P(B) = 0.8 {∵A and B are independent}

Correct Option: E

Let P(B) = x
Given, P(A∪B) = 0.8 and P(A) = 0.3
⇒ P(A) + P(B) - P(A∩B) = 0.8
⇒ P(A) + P(B) - P(A) P(B) = 0.8 {∵A and B are independent}
⇒ 0.3 + x - 0.3x = 0.8
⇒ 0.7x = 0.5
∴ x = 5/7

Let the number of green marble = x
Then, Probability of getting a green marble
= ^xc₁ / ²⁴c₁ = 2/3

Correct Option: D

Let the number of green marble = x
Then, Probability of getting a green marble
= ^xc₁ / ²⁴c₁ = 2/3
⇒ x/24 = 2/3
⇒ x = 16

Here, total balls are 14.
∴ Required probability = (³c₁ + ⁷c₁) / ¹⁴c₁

Correct Option: C

Here, total balls are 14.
∴ Required probability = (³c₁ + ⁷c₁) / ¹⁴c₁
= (3 + 7)/14
= 10/14
= 5/7