Question

how do you calculate the probability of two independent events happening consecutively, such as flipping heads then rolling a 6?
a. subtract the probability of one event from the other
b. add the probability of each event
c. multiply the probability of each event
d. divide the probability of one event by the other

Explanation:

For two independent events \(A\) and \(B\), the probability of both \(A\) and \(B\) occurring is given by the formula \(P(A\cap B)=P(A)\times P(B)\). For example, the probability of flipping heads (a fair coin, \(P(\text{heads})=\frac{1}{2}\)) and then rolling a 6 (a fair die, \(P(6)=\frac{1}{6}\)) is \(\frac{1}{2}\times\frac{1}{6}\). Subtracting (option a) is not a valid operation for independent - event probabilities. Adding (option b) is for mutually - exclusive events (finding \(P(A\cup B)\) when \(A\) and \(B\) are mutually exclusive: \(P(A\cup B)=P(A)+P(B)\)). Dividing (option d) has no basis in the formula for independent - event probabilities.

Answer:

C. Multiply the probability of each event