KCET 2025 Math Paper

To enhance understanding of the statements, let's examine each one in detail:
Statement (I): If events E and F are independent, the complements of these events, E′ and F′, are also independent. This statement is true.
When two events, E and F , are independent, the occurrence of one does not affect the likelihood of the other occurring, mathematically expressed as P(E∩F)=P(E)×P(F) Similarly, the complements of these events, E′ and F′, retain this independence property.
Statement (II): Two mutually exclusive events cannot be independent if they have non-zero probabilities. This statement holds true.
Mutually exclusive events are defined by A∩B=emptyset, which implies P(A∩B)=0. For these events to be independent, it would require P(A∩B)=P(A)×P(B). However, if P(A)≠0 and P(B)≠0, then P(A∩B)≠0, contradicting the independence condition. Thus, two non-zero mutually exclusive events cannot be independent.
Conclusively, Statement I is true and Statement II is also true.