Mathematics
Mathematics
Problem
A fair coin is tossed twice. A student claims that the probability of getting at least one head is because, according to the student, only two situations are possible: “at least one head” or “no head.” Answer the following questions to analyse this claim. a. (i) List all possible ordered pairs of outcomes when the coin is tossed twice. b. (ii) Using your list, explain clearly why the student’s argument is incorrect. c. (iii) Calculate the correct probability of obtaining at least one head in the two tosses.Intuitive explanation
The student is confusing equally likely outcomes with equally likely events. When you toss a coin twice, there are actually four equally likely outcomes (HH, HT, TH, TT), not two. The key insight is that "at least one head" and "no heads" don't occur with equal probability because they don't represent equal numbers of those basic outcomes. Counting carefully which outcomes fall into each category will reveal the true probability.
Intuitive explanation
The student is confusing equally likely outcomes with equally likely events. When you toss a coin twice, there are actually four equally likely outcomes (HH, HT, TH, TT), not two. The key insight is that "at least one head" and "no heads" don't occur with equal probability because they don't represent equal numbers of those basic outcomes. Counting carefully which outcomes fall into each category will reveal the true probability.