Question

A fair coin tossed repeatedly. If the tail appears on the first four tosses, then the probability of head appearing on the fifth toss equals
(A) \[\dfrac{1}{2}\]
(B) \[\dfrac{1}{{32}}\]
(C) \[\dfrac{{31}}{{32}}\]
(D) \[\dfrac{1}{5}\]

Answer 1

Hint: Here we are asked to find the probability of getting head on fifth toss when the coin is tossed repeatedly. First, we must know the sample space of tossing a coin. The probability of single coin tossed n number if times gives same result. Thus, if the coin is tossed for a fifth time the sample space will be the same. Using this we will find the required probability and find the correct option.

Formula:
Formula that we need to know:
$P(E) = $ Number of favourable cases $/$ Total number of cases.

Complete answer:
Probability is the part of arithmetic concerning mathematical portrayals of how probable an occasion is to happen, or how conceivable it is that a recommendation is valid. The probability of an occasion is a number somewhere in the range of 0 and 1, where, generally talking, 0 shows inconceivability of the occasion and 1 demonstrates sureness in the occasion or the definite occasion.
If a coin is flipped, the probability of getting a head is $\dfrac{1}{2}$
similarly, if we toss a coin and the probability of getting a tail is $\dfrac{1}{2}$
Now we can see from our observation that,
The event of heads appearing on the fifth flip is independent of the event that the tail appears on the first four tosses.
So, it does not matter what was the result of the first four tosses,
If the fifth result is independent of the first four.
Hence, the probability of heads appearing on the fifth flip is $\dfrac{1}{2}$

Therefore, the required answer is option (A) i.e., $\dfrac{1}{2}$

Note:
While solving such questions we need to keep in mind that whether the event that is occurring is independent or dependent on the events that have occurred earlier or in the past. Another important thing to be kept in mind is the basic formula of probability i.e., Number of favourable cases/ Total number of cases and to make the table of the same.