Which of the following arguments are correct and which are not correct? Give reasons for your answer.

(i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is $\dfrac{1}{3}$.

(ii) If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is $\dfrac{1}{2}$.

(i) The above statement is incorrect.

We can classify the outcomes like this but they are not then 'equally likely'. Reason is that ‘one of each’ can result in two ways — from a head on first coin and tail on the second coin or from a tail on the first coin and head on the second coin. This makes it twice as likely as two heads (or two tails).

(ii) The above statement is correct.

As, on tossing a die,

Sample space = {1, 2, 3, 4, 5, 6}.

Total possible outcomes = 6

Odd numbers = 3 {1, 3, 5}

Even numbers = 3 {2, 4, 6}.

P(odd numbers) = P(even numbers) = $\dfrac{3}{6} = \dfrac{1}{2}$.