Question

1. which formulas are used to calculate the probability of compound events without adjustment?

a. ( p(a)+p(b) )
b. ( p(a \text{ and } b)=p(a)\times p(b) )
c. ( p(a)-p(b) )
d. ( \frac{p(a)}{p(b)} )

Explanation:

• For independent events \(A\) and \(B\), the probability of both \(A\) and \(B\) occurring (compound event) is given by the formula \(P(A\ and\ B)=P(A)\times P(B)\).
• Option \(a\) \(P(A)+P(B)\) is the formula for the probability of mutually - exclusive events \(A\) or \(B\) (not for compound events \(A\) and \(B\)).
• Option \(c\) \(P(A) - P(B)\) has no direct relation to compound - event probability.
• Option \(d\) \(\frac{P(A)}{P(B)}\) is not a standard formula for compound - event probability.

Answer:

B. \(P(A\ and\ B)=P(A)\times P(B)\)