Final answer:
The question pertains to various probability formulas for calculating the likelihood of multiple events. Formulas for independent events and mutually exclusive events both use multiplication and addition rules respectively; P(r1) * P(r2) * P(r3) * P(r4) for independent events all occurring, and combining with 'and' or 'or' for compound events.
Step-by-step explanation:
Understanding Probability Formulas
The question concerns different probability formulas related to the likelihood of multiple events occurring, which can be calculated using multiplication or addition rules depending on whether they are independent or mutually exclusive.
The formula P(r₁) * P(r₂) * P(r₃) * P(r₄) applies when each event r₁, r₂, r₃, and r₄ is independent, and you want to find the probability of all occurring at the same time. The formula P(r₁ ∩ r₂ ∩ r₃ ∩ r₄) also expresses the probability of all four events occurring together, with ∩ denoting 'and'.
The formula P(r₁ ∪ r₂ ∪ r₃ ∪ r₄) calculates the probability of at least one of the events happening, with ∪ meaning 'or'. The formula P(r₁ ∩ r₂ ∪ r₃ ∩ r₄) refers to the probability of either the first two events occurring together or the last two occurring together. Each formula is used in different scenarios and it's important to understand the context to choose the correct one.
The probability of an event occurring can be calculated using different formulas depending on the specific situation. In this case, the formulas for calculating the probability of different combinations of events are:
a. P(r₁) * P(r₂) * P(r₃) * P(r₄)
b. P(r₁ ∩ r₂ ∩ r₃ ∩ r₄)
c. P(r₁ ∪ r₂ ∪ r₃ ∪ r₄)
d. P(r₁ ∩ r₂ ∪ r₃ ∩ r₄)
These formulas involve multiplying probabilities, calculating the intersection of events, and calculating the union of events. By substituting the appropriate probabilities into these formulas, you can determine the probability of different outcomes.