Late shows some tv shows begin after their scheduled times when earlier programs run late. according to a network’s records, about 3% of its shows start late. to find the probability that three consecutive shows on this network start on time, can we multiply (0.97)(0.97)(0.97)? why or why not?

No because the probability of consecutive shows starting late are not independent events

Step-by-step explanation:

Is good begin with the definition of independent events

When we say Independent Events we are refering to  events which occur with no dependency of other evnts. Basically when the occurrence of one event is not affected by another one.

When two events are independent P(A and B) = P(A)xP(B)

But for this case we can't multiply 0.97x0.97x0.97 in order to find the probability that 3 consecutive shows start on time, because the probability for shows starting late are not independent events, because if the second show is late, the probability that the next show would be late is higher. And for this reason we can use the independency concept here and the multiplication of probabilities in order to find the probability required.