Problem:
A coin is tossed again and again. If tail appears on the first three tosses, then the chance that a head appears on the fourth toss is:
a) 1/16
b) 1/8
c) 1/2
d) 1/4

Solution:
To solve this problem, let's consider the possible outcomes of a coin toss. A coin has two sides - heads and tails. So, when we toss a coin, there are two possible outcomes - either it lands heads up or tails up.

Possible Outcomes:
When a coin is tossed, there are a total of 2^4 = 16 possible outcomes since each toss has 2 possibilities (heads or tails) and there are 4 tosses in total.

Outcomes with Tail on First 3 Tosses:
We are given that the first three tosses result in tails. So, let's consider the outcomes where tails appear on the first three tosses.

There is only one outcome where tails appear on all three tosses, which is TTTT.

Possible Outcomes with Tails on First 3 Tosses:
1. TTTT (tails on all four tosses)

Outcomes with Head on Fourth Toss:
Now, out of the above outcomes, we need to find the ones where a head appears on the fourth toss.

Since there is only one outcome where tails appear on the first three tosses, we need to figure out how many of these outcomes have a head on the fourth toss.

Possible Outcomes with Head on Fourth Toss:
1. TTTT (tails on first three tosses, head on fourth toss)

Probability Calculation:
The probability of an event occurring is given by the number of favorable outcomes divided by the total number of possible outcomes.

In this case, there is only one favorable outcome (tails on first three tosses, head on fourth toss) out of 16 possible outcomes.

Therefore, the probability of a head appearing on the fourth toss, given that tails appear on the first three tosses, is 1/16.

Hence, the correct answer is option a) 1/16.