Question

Mating eagle pairs typically have two baby eagles (called eaglets). When there are two eaglets, the parents always feed the older eaglet until it has had its fill, and then they feed the younger eaglet. This results in an unequal chance of survival for the two eaglets. Suppose that the older eaglet has a 50 percent chance of survival. If the older eaglet survives, the younger eaglet has a 10 percent chance of survival. If the older eaglet does not survive, the younger eaglet has a 30 percent chance of survival. Let X be the number of eaglets that survive. Which of the following tables shows the probability distribution of X?A. x 0 1 2 p(x) 1/3 1/3 1/3B. x 0 1 2 p(x) 1/4 1/2 1/4C. x 0 1 2 p(x) 0.35 0.60 0.05D. x 0 1 2 p(x) 0.05 0.90 0.05E. x 0 1 2 p(x) 0.10 0.30 0.50

Answer 1

Answer:

C. x 0 1 2 p(x) 0.35 0.60 0.05

Step-by-step explanation:

50% chance of survival

Let:

x = older eaglet survive

y = younger eaglet survive

Hence,

P(x = 0) (none of the eaglet survive)

P(x = 1) (only one survive)

P(x = 2) (both survive)

P(x) = 0.5

P(x') = 1 - 0.5 = 0.5

P(x n y) = 0.5 * 0.1 = 0.05 ( both survive)

P(only one survive)

P(y n x') + p(y' n x)

(0.5 * 0.3) + (0.5 * (1 - 0.1))

0.15 + 0.45 = 0.6

P(none survives)

1 - (0.60 + 0.05)

= 0.35

X _______ 0 ______ 1 ______ 2

P(x) ____ 0.35 ____ 0.60 ___ 0.05