Final answer:
To calculate the probability of Madhu being upgraded at least once in the next 25 flights, we can subtract the probability of her not being upgraded at all from 1. Each flight is an independent event, so we can use the rule for calculating the probability of multiple independent events happening.
Step-by-step explanation:
To calculate the probability of Madhu being upgraded at least once in the next 25 flights, we first need to determine the probability of her not being upgraded on each individual flight. From the information provided, we know that initially only 50% of the passengers make the correct choice and go up to the junction. However, even those who initially go down still have a chance to wander back up before time expires. Since effectively 75% of the passengers make it to the junction, the probability of Madhu not being upgraded on a single flight is 1 - 0.75 = 0.25.
Since each flight is an independent event, we can use the rule for calculating the probability of multiple independent events happening to find the probability that Madhu is not upgraded on any of the 25 flights. Using the formula P(event not happening) = (1 - probability of event happening), we find that the probability of Madhu not being upgraded on any of the 25 flights is (0.25)^25.
Finally, to find the probability that Madhu will be upgraded at least once in the next 25 flights, we can subtract the probability of her not being upgraded at all from 1, thus giving us a probability of 1 - (0.25)^25.