Problem: On tossing 7 unbiased coins together, what is the probability of getting more tails than heads?

Solution:

To solve this problem, we need to calculate the probability of getting more tails than heads when tossing 7 unbiased coins together.

Step 1: Find the total number of possible outcomes:
When tossing a coin, there are 2 possible outcomes - either a head or a tail. Since we are tossing 7 coins together, the total number of possible outcomes is 2^7 = 128.

Step 2: Find the number of favorable outcomes:
To find the number of favorable outcomes, we need to determine the number of ways in which we can get more tails than heads.

Case 1: 4 tails and 3 heads:
There are 7 coins in total, and we need to find the number of ways to arrange 4 tails and 3 heads among them. We can use the concept of combinations to calculate this. The number of ways to choose 4 tails out of 7 coins is given by C(7, 4) = 7! / (4! * (7-4)!) = 7! / (4! * 3!) = 35.

Case 2: 5 tails and 2 heads:
Similarly, the number of ways to choose 5 tails out of 7 coins is given by C(7, 5) = 7! / (5! * (7-5)!) = 7! / (5! * 2!) = 21.

Case 3: 6 tails and 1 head:
The number of ways to choose 6 tails out of 7 coins is given by C(7, 6) = 7! / (6! * (7-6)!) = 7! / (6! * 1!) = 7.

Case 4: 7 tails and 0 heads:
The number of ways to choose 7 tails out of 7 coins is given by C(7, 7) = 7! / (7! * (7-7)!) = 7! / (7! * 0!) = 1.

Total number of favorable outcomes:
Adding up the number of favorable outcomes from all the cases, we get 35 + 21 + 7 + 1 = 64.

Step 3: Calculate the probability:
The probability of getting more tails than heads is given by the number of favorable outcomes divided by the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 64 / 128
Probability = 1/2

Therefore, the correct answer is option 'A' - 1/2.