Question

Examine the following statements and comment:
If two coins are tossed at the same time, there are $3$ possible outcomes- two heads, two tails, or one of each. Therefore, for each outcome, the probability of occurrence is $1/3$.

Answer 1

The 3 possible outcomes as per the given statement are two heads, two tails, or one of each.

The Probability of two heads, $P\left(HH\right)=P\left(TT\right)=\frac{1}{4}$

Therefore, Probability of one of each $=1-\frac{1}{4}-\frac{1}{4}=\frac{1}{2}$

Hence, the given probabilities of $3$ possible outcomes are not the same.

We usually classify the cases as given in the question. But not here as the event 'one of each' is twice as likely to occur as the remaining two.