Question

A coin is tossed again and again. If the tail appears on the first three tosses, then what is the chance that head appears on the fourth toss?
(a). \[\dfrac{1}{{16}}\]
(b). \[\dfrac{1}{2}\]
(c). \[\dfrac{1}{8}\]
(d). \[\dfrac{1}{4}\]

Answer 1

Hint: Determine if the two events, that is, tail appearing on the first three tosses and head appearing on the fourth toss are independent. Then, find the probability that the head appears on the fourth toss.

Complete step-by-step answer:
Probability is the measure of how likely an event will occur.
The experiment is a series of actions where the outcomes are always uncertain. An example is the tossing of a coin.
The formula for probability P(E) is the number of favorable outcomes N(E) divided by the total number of outcomes N(S).
\[P(E) = \dfrac{{N(E)}}{{N(S)}}............(1)\]
Events are said to be independent if the occurrence or non-occurrence of one does not affect the occurrence or non-occurrence of the other.
In the given problem, the coin is tossed four times. It is given that the tail appears on the first three tosses.
We need to find what is the chance of heads to appear in the fourth toss.
We know that the event of tossing a coin is an independent event. The fourth coin toss doesn’t depend on the first three and hence, is not affected by the first three tosses.
Hence, the two possible outcomes on the fourth toss are head or tail.
\[N(S) = 2..........(2)\]
Let E be the event that the head occurs.
\[N(E) = 2..........(3)\]
Substituting equations (2) and (3) in equation (1), we get:
\[P(E) = \dfrac{1}{2}\]
Hence, the correct answer is option (c).

Note: Do not attempt to solve the question based on the appearance of tails on the first three tosses. It is given to confuse you, the fourth toss is an independent event.