Probability Questions and Answers

x

Option: D

Explanation

n(S) = number of ways of drawing 3 marbles out of 12

n(S) = ¹²C₃ = (12 * 11 * 10)/(3 * 2 * 1) = 220

E = event of drawing (3 marbles out of 5) or (3 marbles out of 4) or (3 marbles out of 3)

n(E) = ⁵C₃ + ⁴C₃ + ³C₃=⁵C₂ + ⁴C₁ + 1 = ((5 * 4)/(2 * 1)) + 4 + 1 = 15

P(E) = n(E)/n(S) = 15/220 = 3/44

x

Option: A

Explanation

n(S) = number of ways of drawing 2 balls out of 7

n(S) = ⁷C₂ = (7 * 6)/(2 * 1) = 21

n(E) = number of ways of drawing 2 balls out of (2 + 3) balls

n(E) = ⁵C₂ = (5 * 4)/(2 * 1) = 10

P(E) = n(E)/n(S) = 10/21

x

Option: B

Explanation

n(S) = 21 balls

E = event that the ball drawn is red

n(E) = 8 red balls

P(E) = n(E)/n(S) = 8/21