Question

Three unbiased coins are tossed. What is the probability of getting at most two heads?

Answer 1

Hint: - By the term unbiased coins, the question means that the coins that are being used are not tempered and are normal coins that are available everywhere.
By the term at most, the question means that the number of heads that should be present for the favorable outcomes should be either 0 or 1 or 2.

Complete step-by-step answer:
The most important formula that would be used to evaluate the answer is the formula for evaluating the probability of any event and that is as follows
P \[=\dfrac{Favorable\ outcomes}{Total\ outcomes}\]
As mentioned in the question, we have to find the probability of getting at most two heads.
So, the total outcomes for the event tossing three unbiased coins are as follows
Total outcomes = (h, h, h), (h, h, t), (h, t, h), (t, h, h), (h, t, t), (t, t, h), (t, h, t), (t, t, t)
(Where ‘h’ represents head and ‘t’ represents tail)
Total outcomes \[=8\] .
Now, for favorable outcomes, we need to count the total number of cases in which the head comes at most two times, so, the favorable outcomes are the following
(h, h, t), (h, t, h), (t, h, h), (h, t, t), (t, t, h), (t, h, t), (t, t, t)
Favorable outcomes \[=7\] .

Now, using the formula for calculating the probability of getting at most two heads, we get
 \[\begin{align}
  & =\dfrac{Favorable\ outcomes}{Total\ outcomes} \\
 & =\dfrac{7}{8} \\
\end{align}\]
Hence, the probability of getting at most two heads is \[\dfrac{7}{8}\] .

Note: -Similarly, we can calculate the probability of getting a blue ball or the probability of getting a white ball from the box by using the same formula as mentioned in the hint and the solution as well.
 The only difference in the other two probabilities would be that only the favorable outcomes would be changing according to the event.
Another method of doing this question is by finding the probability of getting three heads and then we will subtract it from 1.