Total Number of outcomes = ¹⁰C₃ = 120
Number of outcomes not containing red balls = ⁵C₃ = 10
∴ Probability that at least one is red = 1 - 10/120

Correct Option: C

Total Number of outcomes = ¹⁰C₃ = 120
Number of outcomes not containing red balls = ⁵C₃ = 10
∴ Probability that at least one is red = 1 - 10/120 = 11/12

Total number of outcomes = ¹⁰c₄ = 210
Favourable number of outcomes = ³c₂ x ²c₂

Correct Option: B

Total number of outcomes = ¹⁰c₄ = 210
Favourable number of outcomes = ³c₂ x ²c₂ = 3 x 1 = 3
∴ Required probability = 3/210 = 1/70

n(S) = Number of ways of drawing 2 cards out of 52
⁵²C₂ = (52 x 51) / (2 x 1) = 1326
n(E) = Number of ways of drawing 2 cards out of 4
= ⁴C₂ = (4 x 3)/2 = 6

Correct Option: A

n(S) = Number of ways of drawing 2 cards out of 52
⁵²C₂ = (52 x 51) / (2 x 1) = 1326
n(E) = Number of ways of drawing 2 cards out of 4
= ⁴C₂ = (4 x 3)/2 = 6
∴ P(E) = 6/1326 = 1/221

There are 13 hearts and 3 more kings
∴ P(heart or a king) = (13 + 3)/52 = 4/13

Correct Option: B

There are 13 hearts and 3 more kings
∴ P(heart or a king) = (13 + 3)/52 = 4/13
∴ P (neither a heart nor a king) = 1 - 4/13 = 9/13

You can have
W, W, B or W, B, W or B, W, W

Correct Option: A

You can have
W, W, B or W, B, W or B, W, W

Reqd. probability
= 3/4. 2/4. 3/4 + 3/4. 2/4. 1/4 + 1/4. 2/4. 1/4
= 9/32 + 3/32 + 1/32 = 13/32