Final answer:
The statement about wave superposition with different frequencies is true; they can interfere and form complex patterns. The statement about wave amplitude being affected only when waves are precisely aligned is false, as waves can superpose in any alignment. Two mutually exclusive events G and H cannot both occur, making P(H|G) = .4 false and as mutually exclusive events, they are dependent.
Step-by-step explanation:
The statement that waves can superimpose if their frequencies are different is true. When two waves of different frequencies meet, they superimpose on each other, resulting in a phenomenon known as interference. This can lead to various effects, such as the creation of standing waves, beat frequencies, or complex wave patterns.
The statement that the amplitude of one wave is affected by the amplitude of another wave only when they are precisely aligned is false. Superposition of waves can occur regardless of whether they are perfectly aligned or not. The resultant amplitude at any point is the vector sum of the amplitudes of the individual waves at that point.
Regarding probabilities, two events G and H are said to be mutually exclusive if they cannot occur at the same time. If P(G) = .5 and P(H) = .3, the statement that P(H|G) = .4 must be false since the conditional probability P(H|G) represents the probability of H occurring given that G has occurred, which would be zero for mutually exclusive events. Consequently, the probability P(H OR G) would be the sum of their individual probabilities, which is .5 + .3 = .8, assuming that there are no other events that G and H can be part of. As mutually exclusive events, G and H are also dependent events because the occurrence (or non-occurrence) of one affects the probability of the other.