Final answer:
To find the probability of events a and b, we can use the equation P(a AND b) = P(a) * P(b), and solve for P(a).
Step-by-step explanation:
In this question, we are given that events a and b are equally likely, and we are required to find the probability of their intersection.
Since a and b are equally likely, we can assume that P(a) = P(b).
Let x be the probability of event a. Then, the probability of event b is also x.
Since the probability of their intersection is at least 0.98, we have:
P(a AND b) = P(a) * P(b) >= 0.98
Since P(a) = P(b) = x, we substitute to get:
x * x >= 0.98
x^2 >= 0.98
Taking the square root of both sides:
x >= sqrt(0.98)
Therefore, the probability of event a (P(a)) is greater than or equal to the square root of 0.98.