To study the migration of adult Pacific salmons, researchers tag salmons with electronic transmitters that track individual fish throughout their migration. Underwater receivers are built at various locations along the river to receive the signal from these electronic transmitters. At a location where a river diverges into distributaries, two independent receivers A and B are used at to detect and locate these salmons. The probability that receiver A receives the signal from a fish is 0.8, whereas the corresponding probability of receiver B is 0.9.

(a) What is the probability that the signal from a fish will be received? [5 marks]

(b) What is the probability that the signal from a fish will be received by only one receiver? [5

marks]

(When answering the questions, writing down the final answer will not be sufficient to receive full marks. Please show all calculations unless otherwise specified. Also define any events and notation that you use in your solutions.)

To study the migration of adult Pacic salmons, researchers tag salmons with electronic transmitters that track individual sh throughout their migration. Underwater receivers are built at various locations along the river to receive the signal from these electronic transmitters. At a location where a river diverges into distributaries, two independent receivers A and B are used at to detect and locate these salmons. The probability that receiver A receives the signal from a sh is 0.8, whereas the corresponding probability of receiver B is 0.9. (a) What is the probability that the signal from a sh will be received? [5 marks] (b) What is the probability that the signal from a sh will be received by only one receiver? [5 marks]