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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

Respuesta :

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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

The probability distribution of the number of eaglets is the set of the

probabilities of the number of surviving eaglets.

The table that shows the probability distribution is the option C;

[tex]C. \ \overline{\underline{\begin{array}{|c|c|c|c|}x&0&1&2\\P(x)&0.35&0.60&0.05\end{array}\right] }}[/tex]

Reasons:

The probability that the older eaglet survives P(O) = 0.5

Therefore;

The probability that the older eaglet does not survives P(O') = 1 - 0.5 = 0.5

The chance of survival of the younger eaglet, where the older eaglet survives P(Y|O) = 10%

Therefore;

The chance that the younger eaglet does not survive, where the older eaglet survives P(Y'|O) = 1 - 10% = 90%

The chance of survival of the younger eaglet, where the older eaglet does not survives P(Y|O') = 30%

Therefore;

The chance that the younger eaglet does not survive, where the older eaglet does not survives P(Y'|O') = 1 - 30% = 70%

The probability distribution, P(X) is the set of possible probability of the number of eaglets that survive, which is given as follows;

The set of possible outcomes are;

Non survives:

  • The probability that non of the eaglets survives = P(O') × P(Y'|O') = 0.5 × 0.7 = 0.35

Only one survives:

  • The probability that only one of the eaglet survives = P(O) × P(Y'|O) + P(O') × P(Y|O'), which gives; P = 0.5 × 0.9 + 0.5 × 0.3 = 0.6

Both survives:

  • The probability that both of the eaglet survives = P(O) × P(Y|O) = 0.5 × 0.1 = 0.05

The table of the probability distribution is therefore;

[tex]C. \ \overline{\underline{\begin{array}{|c|c|c|c|}x&0&1&2\\P(x)&0.35&0.60&0.05\end{array}\right] }}[/tex]

Learn more here:

https://brainly.com/question/17466045

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