Question

A₁,A₂,...,A₁₅ are independent events, each having probability p of occurring. Which of the following expressions for P(A₁ UA₂ U... U A₁₅) is correct?

a. 1-(1 - p)¹⁵
b. 15p
c. p¹⁵
d. (1-p)¹⁵

Answer 1

The correct expression for the probability of the union of independent events is 1-(1 - p)¹⁵.

Step-by-step explanation:

To find the probability of the union of independent events, you can use the formula P(A₁ UA₂ U... U A₁₅) = 1 - (1 - p)¹⁵. This means that the probability of at least one of the events occurring is equal to 1 minus the probability that none of the events occur. So, the correct expression is a. 1-(1 - p)¹⁵.