Mathematics, 07.06.2021 23:20, butryn

Seventy-six percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 67% have an emergency locator, whereas 88% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. (Round your answers to three decimal places.) Required:
a. If it has an emergency locator, what is the probability that it will not be discovered?
b. If it does not have an emergency locator, what is the probability that it will be discovered?

Answers: 3

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Answers

answered: Dragonfierz666

a. 0.0535 = 5.35% probability that it will not be discovered

b. 0.9465 = 94.65% probability that it will be discovered

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

a. If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator.

Event B: Not discovered.

Probability of having an emergency locator:

67% of 76%(discovered).

100 - 88 = 12% of 100 - 76 = 24%(not discovered). So

P(A) = 0.67*0.76 + 0.12*0.24 = 0.538

Probability of having an emergency locator and not being discovered:

12% of 24%. So

$P(A \cap B) = 0.12*0.24$

Desired probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.12*0.24}{0.538} = 0.0535$

0.0535 = 5.35% probability that it will not be discovered.

b. If it does not have an emergency locator, what is the probability that it will be discovered?

Event A: Has an emergency locator.

Event B: Discovered.

Probability of having an emergency locator:

67% of 76%(discovered).

100 - 88 = 12% of 100 - 76 = 24%(not discovered). So

P(A) = 0.67*0.76 + 0.12*0.24 = 0.538

Probability of having an emergency locator not being discovered:

67% of 76%. So

$P(A \cap B) = 0.67*0.76$

Desired probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.67*0.76}{0.538} = 0.9465$

0.9465 = 94.65% probability that it will be discovered

answered: Guest

use an equation of ratios to determine the amount of gas needed to fill the tank.

0.2 0.8

288.75 x

231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal $3

* = $3465 (answer)

1 1 gal

hope this you

answered: Guest

step-by-step explanation:

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Seventy-six percent of the light aircraft that disappear while in flight in a certain country are su...