I throw two coins (simultaneously). A student (very much a beginner in both math and probability theory) thought that the following 3 outcomes are equally likely: "two heads", "two tails", "a head and a tail".
However much I tried, I couldn't find a clear and obvious explanation of why it's not the case.
Of course, I could say the coins are distinct, so we need to look at how each individual coin falls (leading to 4 equally likely outcomes: HH, HT, TH, TT). But I couldn't clearly explain the concept of "distinct" and why it's important for the probability calculation.
Anyone can help with a simple, precise and very intuitive explanation?