Which of the following arguments are correct and which are not correct? Give reasons for your answers.
(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) Not correct. The equally likely outcomes are HH, HT, TH and TT, so P(two heads) = 1/4, P(two tails) = 1/4 and P(one of each) = \(\dfrac{1}{2}\), not \(\dfrac{1}{3}\) each.
(ii) Correct. There are three odd (1, 3, 5) and three even (2, 4, 6) outcomes, so P(odd) = \(\dfrac{3}{6}\) = \(\dfrac{1}{2}\).