Final answer:
The subsets of the set S={E,F,G} include the empty set, each individual element, every combination of two elements, and the set itself. Probabilities like P(G) and P(G OR E) depend on additional context, and events are mutually exclusive if they cannot occur simultaneously, reflected by P(G AND E) = 0.
Step-by-step explanation:
Understanding Subsets and Probability
To list all the subsets of the set S = {E, F, G}, we begin by noting that a set with n elements has 2^n subsets, including the empty set and the set itself. In this case, S has 3 elements, so there will be 2^3 = 8 subsets. These subsets are:
{} (the empty set)
{E}
{F}
{G}
{E, F}
{E, G}
{F, G}
{E, F, G} (the set itself)
To discuss probabilities such as P(G), P(G|E), P(G AND E), and P(G OR E), we need information about a particular experiment or sample space. Events G and E are mutually exclusive if they cannot occur at the same time, which is numerically justified when P(G AND E) = 0. When no further context is provided, these probabilities cannot be calculated.
For mutually exclusive events such as F and G in a different context, we would also need specific probabilities to answer this. Finally, when considering events with numerical outcomes like in a deck of cards or dice, to calculate the probability of an event, we count the favorable outcomes and divide by the total number of outcomes in the sample space.