Find the (theoretical) probability of the given event, assuming that the coins are distinguishable and fair, and that what is observed are the faces uppermost.

Six coins are tossed; the result is at most one head.

To find the probability of getting at most one head when tossing six coins, we need to determine the number of favorable outcomes (getting 0 or 1 heads) and divide it by the total number of possible outcomes.

Number of favorable outcomes:
To get 0 heads, all six coins must land on tails. This is only one possible outcome.

To get 1 head, there are six different coins that could land on heads, and the other five coins must land on tails. So, there are six possible outcomes for this scenario.

Total number of possible outcomes:
Each of the six coins has two possible outcomes: heads or tails. So, the total number of possibilities when tossing six coins is 2^6 = 64.

Therefore, the probability of getting at most one head when tossing six coins is (number of favorable outcomes) / (total number of possible outcomes) = (1 + 6) / 64 = 7 / 64.

Hence, the theoretical probability of this event is 7/64.

To find the probability of obtaining at most one head when tossing six coins, we need to consider all possible outcomes and determine how many of them satisfy this condition.

Since each coin can either land on heads or tails, there are 2^6 = 64 possible outcomes when tossing six coins. To simplify the calculation, we can use the concept of combinations.

Let's evaluate the number of outcomes where we get at most one head:

1. Zero heads: This can only occur in one way, which is when all six coins land on tails.

2. One head: There are six positions where the head can appear (the first, second, third, fourth, fifth, or sixth coin). Therefore, there are 6 possible outcomes with one head.

Thus, the total number of favorable outcomes (outcomes with at most one head) is 1 + 6 = 7.

Therefore, the probability of obtaining at most one head when tossing six coins is 7/64.

To calculate this, divide the number of favorable outcomes (7) by the total number of possible outcomes (64):

P(at most one head) = 7/64 ≈ 0.1094

So, the theoretical probability of obtaining at most one head when tossing six distinguishable and fair coins is approximately 0.1094 or 10.94%.