A ball is selected at random from 10 black and 5 red balls. The ball- i. has probability 1/3 of being red ii. has probability 2/3 of not being red iii. has probability 1 of being red or black

Cumilla Board 2023

A ball is selected at random from 10 black and 5 red balls. The ball-

Think it through first, then pick an option.

Answer and explanation

Correct answer: d i, ii and iii

i is true: 5 red out of 15, 5/15 = 1/3; ii is true: 1 − 1/3 = 2/3 (or 10/15); iii is true: every ball is red or black, so the event is certain.

Why the other options are wrong

a i and ii: iii is true (every ball is red or black, so the event is certain), so iii has to be in the combination; the combination is i, ii and iii.
b i and iii: ii is true (1 − 1/3 = 2/3 (or 10/15)), so ii has to be in the combination; the combination is i, ii and iii.
c ii and iii: i is true (5 red out of 15, 5/15 = 1/3), so i has to be in the combination; the combination is i, ii and iii.