There are three boxes. The first box has 2 white, 3 black and 4 red balls. The second box has 3 white, 2 black and 2 red balls. The third box has 4 white, 1 black and 3 red balls. A box is chosen at random and 2 balls are drawn, of which 1 is white and 1 is red. What is the probability that the balls came from the first box?
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: A. 0.237
Explanation
P(E|B1) = (2×4)/C(9,2) = 8/36 = 2/9; P(E|B2) = (3×2)/C(7,2) = 6/21 = 2/7; P(E|B3) = (4×3)/C(8,2) = 12/28 = 3/7. By Bayes: (2/9) / (2/9 + 2/7 + 3/7) = 14/59 ≈ 0.237.More Discrete Structures and Optimisation questions
- Consider the primal problem: Maximize z = 5x1 + 12x2 + 4x3 subject to x1 + 2x2 + x3 = 10 2x1 − x2 + 3x3 = 8 x1, x2, x3 ≥ 0 Its dual problem…
- The logic expression (P′ ∧ Q) ∨ (P ∧ Q′) ∨ (P ∧ Q) is equivalent to
- Consider α, β, γ as logical variables. Which of the following are correct logical equivalences? (A) α ∧ (β ∨ γ) ≡ (α ∧ β) ∨ (α ∧ γ) (B) α ∨…
- Let ({a, b}, *) be a semigroup where a * a = b. Consider: (A) a * b = b * a (B) b * b = b Choose the most appropriate answer from the optio…
- Let ε = 0.0005 and let Rε = {(x, y) ∈ ℝ2 : |x − y| < ε}, which can be interpreted as 'approximately equal'. Rε is (A) Reflexive (B) Symmetr…
- Consider the following in Boolean algebra: X: a ∨ (b ∧ (a ∨ c)) = (a ∨ b) ∧ (a ∨ c) Y: a ∧ (b ∨ (a ∧ c)) = (a ∧ b) ∨ (a ∧ c) The identity a…