One theory of why birds form in flocks is that flocks increase efficiency in scanningfor approaching predators. Because birds can barely move their eyes they must turntheir heads to look for predators, making them temporarily unable to peck for food. Ifthe birds form flocks, each bird could spend less time scanning; when a single birddetects a predator it alerts the other birds.

The Chanting Goshawk is a predator of the Red-billed Weaver bird. From fieldobservation it is estimated that an individual weaver bird has a probability of 0.20 ofdetecting a goshawk in time to fly to safety. Suppose that a goshawk suddenly comesupon a flock of 4 weaver birds pecking for food on the ground, and attacks.

a) What is the probability that none of the weaver birds will detect the goshawk'spresence before it is too late, thus allowing the goshawk to have a weaver birdlunch?

b) What is the probability that at least one of the weaver birds will detect thegoshawk's presence, thus alerting the others and all fly away, leaving thegoshawk hungry?

c) Suppose this is Wednesday, and all weaver birds form flocks of size 4 onWednesdays. Using your results from parts (a) and/or (b), find the probabilitythat a goshawk will go hungry until swooping down on the 5th flock of 4 weaverbirds seen that day.

Question

One theory of why birds form in flocks is that flocks increase efficiency in scanningfor approaching predators. Because birds can barely move their eyes they must turntheir heads to look for predators, making them temporarily unable to peck for food. Ifthe birds form flocks, each bird could spend less time scanning; when a single birddetects a predator it alerts the other birds.

The Chanting Goshawk is a predator of the Red-billed Weaver bird. From fieldobservation it is estimated that an individual weaver bird has a probability of 0.20 ofdetecting a goshawk in time to fly to safety. Suppose that a goshawk suddenly comesupon a flock of 4 weaver birds pecking for food on the ground, and attacks.

a) What is the probability that none of the weaver birds will detect the goshawk'spresence before it is too late, thus allowing the goshawk to have a weaver birdlunch?

b) What is the probability that at least one of the weaver birds will detect thegoshawk's presence, thus alerting the others and all fly away, leaving thegoshawk hungry?

c) Suppose this is Wednesday, and all weaver birds form flocks of size 4 onWednesdays. Using your results from parts (a) and/or (b), find the probabilitythat a goshawk will go hungry until swooping down on the 5th flock of 4 weaverbirds seen that day.

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The Answer of One theory of why birds form in flocks is that flocks increase efficiency in scanningfor approaching predators. Because birds can barely move their eyes they must turntheir heads to look for predators, making them temporarily unable to peck for food. Ifthe birds form flocks, each bird could spend less time scanning; when a single birddetects a predator it alerts the other birds.

The Chanting Goshawk is a predator of the Red-billed Weaver bird. From fieldobservation it is estimated that an individual weaver bird has a probability of 0.20 ofdetecting a goshawk in time to fly to safety. Suppose that a goshawk suddenly comesupon a flock of 4 weaver birds pecking for food on the ground, and attacks.

a) What is the probability that none of the weaver birds will detect the goshawk'spresence before it is too late, thus allowing the goshawk to have a weaver birdlunch?

b) What is the probability that at least one of the weaver birds will detect thegoshawk's presence, thus alerting the others and all fly away, leaving thegoshawk hungry?

c) Suppose this is Wednesday, and all weaver birds form flocks of size 4 onWednesdays. Using your results from parts (a) and/or (b), find the probabilitythat a goshawk will go hungry until swooping down on the 5th flock of 4 weaverbirds seen that day.

One Theory of Why Birds Form in Flocks Is That