Sam commutes to work by bus. He has to make two transfers. Historically, he has to wait more than five minutes for the first transfer 10% of the time. If he has to wait more than five minutes for the first transfer, he has to wait more than five minutes for the second transfer 30% of the time. If he does not have to wait more than five minutes for the first transfer, then he has to wait more tha five minutes for the second transfer 40% of the time. Are the events, wait more than five minutes for the first transfer and wait more than five minutes for the second transfer, independent? a) No. Since the probability of waiting more than five minutes for the second transfer is different depending on whether Sam waits more than five minutes for the first transfer, these events are not independent events.
b) No. Since the probability of waiting more than five minutes for the second transfer is the same regardless of whether Sam waits more than five minutes for the first transfer, these events are not independent.
c) Yes. Since the probability of waiting more than five minutes for the second transfer is different depending on whether Sam waits more than five minutes for the first transfer, these events are independent events.
d) Yes. Since the probability of waiting more than five minutes for the second transfer is the same regardless of whether Sam waits more than five minutes for the first transfer, these events are independent events