Preamble:
The probability of a cricket team winning a match at Kanpur is 2/5 and losing a match at Delhi is 1/7. We need to determine the probability of the team winning at least one match.

Solution:
To find the probability of winning at least one match, we need to consider the possibilities of winning both matches, winning only one match, and losing both matches separately.

Winning both matches:
The probability of winning both matches is the product of the individual probabilities. Therefore, the probability of winning both matches is (2/5) * (2/5) = 4/25.

Losing both matches:
The probability of losing both matches is the product of the individual probabilities. Therefore, the probability of losing both matches is (1/7) * (1/7) = 1/49.

Winning only one match:
To find the probability of winning only one match, we need to consider the possibilities of winning at Kanpur and losing at Delhi, or losing at Kanpur and winning at Delhi.

Probability of winning at Kanpur and losing at Delhi:
The probability of winning at Kanpur is 2/5 and the probability of losing at Delhi is 1/7. Therefore, the probability of winning at Kanpur and losing at Delhi is (2/5) * (1/7) = 2/35.

Probability of losing at Kanpur and winning at Delhi:
The probability of losing at Kanpur is 3/5 (1 - 2/5) and the probability of winning at Delhi is 6/7 (1 - 1/7). Therefore, the probability of losing at Kanpur and winning at Delhi is (3/5) * (6/7) = 18/35.

Calculating the probability of winning at least one match:
To find the probability of winning at least one match, we need to sum up the probabilities of winning both matches, winning only one match, and losing both matches.

Probability of winning at least one match = Probability of winning both matches + Probability of winning only one match + Probability of losing both matches

Probability of winning at least one match = (4/25) + (2/35 + 18/35) + (1/49)

Simplifying the expression, we get:

Probability of winning at least one match = 4/25 + 20/35 + 1/49

To add the fractions, we need to find a common denominator. The least common multiple of 25, 35, and 49 is 1715.

Converting the fractions to have a common denominator:

Probability of winning at least one match = (4/25) * (69/69) + (20/35) * (49/49) + (1/49) * (35/35)

Probability of winning at least one match = 276/1715 + 980/1715 + 35/1715

Adding the fractions together, we get:

Probability of winning at least one match = 1291/1715

Simplifying the fraction, we find:

Probability of winning at least one match = 0.7538

Conclusion:
Therefore, the probability of the cricket team winning at least one match is approximately 0