Final answer:
Waves can superimpose regardless of differing frequencies, which is true. The amplitude of one wave can be affected by another without precise alignment, making the statement false. And for mutually exclusive events G and H, the probability of H given G is 0, making them dependent.The statement is false, b.
Step-by-step explanation:
Understanding Wave Superposition and Probabilities
Firstly, dealing with the aspect of wave physics, the statement 'waves can superimpose if their frequencies are different' is true. When two or more waves encounter each other, they superpose, meaning their amplitudes at a given point in space add together to form a resultant wave. This superposition occurs regardless of whether the waves have the same or different frequencies.
For the probability aspect, consider two events G and H. The concept that 'the amplitude of one wave is affected by the amplitude of another wave only when they are precisely aligned' is false. Waves can affect each other's amplitudes through constructive or destructive interference even if not precisely aligned in time or space.
When dealing with events G and H, a statement such as P(H|G) = .4 for mutually exclusive events is also false. If events are mutually exclusive, the probability of one event given the other has occurred is 0. The probability P(H OR G) for mutual exclusivity can be calculated as P(G) + P(H) since they cannot both occur at the same time. In this case, P(H OR G) = 0.5 + 0.3 = 0.8.
Mutually exclusive events cannot happen simultaneously by definition. If G and H are mutually exclusive, that also implies they are dependent events because the occurrence of one affects the probability of the occurrence of the other.