Question

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?

Short answer

No.

Step-by-step solution

Step 1. Given Information

When previous programmes run late, certain TV programmes start later than scheduled.

Step 2. Concept used

Multiplication rule:$P\left(A\cap B\right)=P\left(A\right)\times P\left(B\right)$

Step 3. Explanation

No, because the likelihood of consecutive shows beginning late is not independent for each show (if the first show starts late, the probability of the next show starting late is increased), and so the general multiplication formula for independent events cannot be used.