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

Solution:
To solve this problem, we need to find the probability of getting at most two tails. Let's break it down step by step.

Step 1: Define the Sample Space
The sample space is the set of all possible outcomes of the coin toss. Since each coin can either land on heads (H) or tails (T), there are 2^3 = 8 possible outcomes:
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Step 2: Determine the Favorable Outcomes
We need to find the number of outcomes in which we get at most two tails. This includes outcomes with zero tails (3 heads) and outcomes with only one tail. The favorable outcomes are:
F = {HHH, HHT, HTH, THH, THT, TTH}

Step 3: Calculate the Probability
The probability of an event is given by the ratio of the number of favorable outcomes to the number of possible outcomes. In this case, the probability of getting at most two tails is:
P(at most two tails) = |F| / |S|

Step 4: Simplify the Probability
Let's calculate the number of elements in the favorable set F and the sample space set S:
|F| = 6
|S| = 8

Now we can substitute these values into the probability formula:
P(at most two tails) = 6 / 8 = 3 / 4

Step 5: Convert to Fraction
To simplify the probability expression, we can write 3/4 as a fraction in the form a/b, where a and b are coprime (they have no common factors other than 1). In this case, we can simplify 3/4 to 3/4 * 1/1 = 3/4 * 2/2 = 6/8.

The final probability of getting at most two tails is 6/8. Now we need to choose the option that represents this probability.

Option Analysis:
a) 7/8
b) 1/2
c) 3/8
d) 1/8

Correct Option:
The correct option is a) 7/8, which matches the probability we calculated.

Conclusion:
The probability of getting at most two tails when three unbiased coins are tossed is 7/8.