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 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 1/2.
Incorrect. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH, and TT (4 outcomes). The outcome 'one of each' can occur in two ways (HT and TH), so the three outcomes mentioned are not equally likely. P(two heads) = 1/4, P(two tails) = 1/4, and P(one of each) = 2/4 = 1/2.
Correct. When a die is thrown, the possible outcomes are 1, 2, 3, 4, 5, 6. There are 3 odd numbers (1, 3, 5) and 3 even numbers (2, 4, 6). Since both odd and even numbers have equal number of outcomes, P(odd number) = 3/6 = 1/2.
Explanation
This question tests understanding of equally likely outcomes. In (i), the student incorrectly groups HT and TH as one outcome, making the three categories appear equally likely when they are not. The correct sample space has 4 equally likely outcomes. In (ii), the die has 6 equally likely outcomes, and odd/even numbers are equally distributed (3 each), making the probability calculation correct.