Question

A dice is loaded so that the probability of face i is proportional to i. i = 1, 2, ....6. Then the probability of an even number occupy when the dice is rolled is _______

(a) (2/7)

(b) (3/7)

(c) (4/7)

(d) (5/7)

Answer 1

The correct option (c) (4/7)  

Explanation:

P(i) ∝ i and i = 1 to 6

∑P(i) = 1

∴ ∑Ki = 1

∴ K∑i = 1 

∴ K(1 + 2 + 3 + 4 + 5 + 6) = 1

∴ K = (1/21)

P(even number on dice) = P(A)

∴ P(A) = P(2) + P(4) + P(6) = 2K + 4K + 6K = 12K

∴ P(A) = 12 × (1/21) = (12/21) = (4/7).