The probability that a ticketless traveller is caught during a rip is 0.1. If the traveller makes 4 trips, the probability that he/she will be caught during at least one of the trips is: 

Correct option is A

Given:

• Probability of being caught in a single trip = 0.1
• Number of trips = 4
• We are to find the probability of being caught at least once in 4 trips

Concept Used:
"At least one" probability questions are often solved using the complement rule:
P(at least one success) = 1 - P(no success at all)

Here,

• Success = getting caught
• Failure = not getting caught = 1 - 0.1 = 0.9
• Probability of not getting caught in all 4 trips = 0.9⁴

Formula Used:
P(at least one caught) = 1 - (Probability of not being caught in any trip)

Solution:
P(not caught in 1 trip) = 0.9
P(not caught in 4 trips) = 0.9 × 0.9 × 0.9 × 0.9 = (0.9)⁴

So,
P(caught at least once) = 1 – (0.9)⁴ 

Final Answer: 1 – (0.9)⁴​