Final answer:
The probability that the migraine medication will be effective in preventing the next 4 headaches is 81.45%, calculated by multiplying the individual probabilities of preventing each headache (0.95) together four times.
Step-by-step explanation:
The question is asking about the probability of a new migraine medication being effective in preventing the next 4 headaches, given that it is effective 95% of the time when taken properly. To calculate this, we can use the concept of independent events in probability theory since the successful prevention of each headache is an independent event.
The probability of the medication preventing one headache is 0.95 (or 95%). Thus, the probability of it preventing 4 headaches in a row is:
0.95 × 0.95 × 0.95 × 0.95 = 0.8145
This means there is an 81.45% chance the medication will be effective in preventing the next 4 severe headaches.