7/8 Probability Topic A

The sample space consists of all possible outcomes, which is 36 outcomes (6 sides on the first die x 6 sides on the second die).

There are 4 possible outcomes: HH, HT, TH, TT.

There are 8 outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

Probability is the measure of the likelihood that an event will occur, calculated as the number of favorable outcomes divided by the total number of outcomes in the sample space.

A tree diagram is a visual representation of all possible outcomes of an event, used to calculate probabilities by branching out each possible outcome.

The formula is: Probability = @@rac{{ ext{Number of favorable outcomes}}}{{ ext{Total number of outcomes}}}.

'Without replacement' means that once an item is drawn from a set, it is not returned to the set before the next draw, affecting the total number of outcomes.

For independent events, the probability of both events occurring is the product of their individual probabilities.