Question

asked Jan 11, 2022 46.1k views

1 Answer

TehK · Answer 1 · 2022-01-16T10:07:06+0000

Answer:

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

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

Explanation:

Conditional Probability

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

$P(B|A) = (P(A \cap B))/(P(A))$

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:

$P(B|A) = (P(A \cap B))/(P(A)) = (0.12*0.24)/(0.538) = 0.0535$

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:

$P(B|A) = (P(A \cap B))/(P(A)) = (0.67*0.76)/(0.538) = 0.9465$

0.9465 = 94.65% probability that it will be discovered

Please log in or register to add a comment.