which of the assignments of probabilities should be used if the coin is known to be fair?

 If a coin is known to be fair, it means that the probability of getting heads (H) is equal to the probability of getting tails (T). In this case, you can use the basic probability formula to calculate the probability of a specific event.

The basic probability formula is:

$�(�)=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

For a fair coin:

• The probability of getting heads (H) is $\frac{1}{2}$ because there is one favorable outcome (H) out of two possible outcomes (H or T).

• The probability of getting tails (T) is also $\frac{1}{2}$ for the same reason.

So, for a fair coin, you can use the following probabilities:

$�(�)=\frac{1}{2}$

$�(�)=\frac{1}{2}$

This assumes that the coin is fair and unbiased, meaning that the outcomes are equally likely. If the coin is known to be fair, the probabilities of getting heads or tails are both $\frac{1}{2}$ or 0.5