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 $\frac{1}{3}$.
(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 $\frac{1}{2}$.
(i) Incorrect
When two coins are tossed, the possible outcomes are (H, H), (H, T), (T, H), and (T, T). It can be observed that there can be one of each in two possible ways − (H, T), (T, H).
Therefore, the probability of getting two heads is $\frac{1}{4}$, the probability of getting two tails is $\frac{1}{4}$, and the probability of getting one of each is $\frac{1}{2}$.
It can be observed that for each outcome, the probability is not $\frac{1}{3}$.
(ii) Correct
When a dice is thrown, the possible outcomes are 1, 2, 3, 4, 5, and 6. Out of these, 1, 3, 5 are odd and 2, 4, 6 are even numbers.
Therefore, the probability of getting an odd number is $\frac{1}{2}$.