B. G. Cosmos,a scientist, believes that the probability is \frac{2}{5} that aliens from an advanced civilization on Planet X are trying to communicate

Question

B. G. Cosmos,a scientist, believes that the probability is \frac{2}{5} that aliens from an advanced civilization on Planet X are trying to communicate

kuCAu 2021-09-19 Answered

B. G. Cosmos, a scientist, believes that the probability is $\frac{2}{5}$ that aliens from an advanced civilization on Planet X are trying to communicate with us by sending high-frequency signals to Earth. By using sophisticated equipment, Cosmos hopes to pick up these signals. The manufacturer of the equipment, Trekee, Inc., claims that if aliens are indeed sending signals, the probability that the equipment will detect them is $\frac{3}{5}$ . However, if aliens are not sending signals, the probability that the equipment will seem to detect such signals is $\frac{1}{10}$ . If the equipment detects signals, what is the probability that aliens are actually sending them?

Ask Expert 1 See Answers

You can still ask an expert for help

Expert Answer

Neelam Wainwright

Answered 2021-09-20 Author has 102 answers

Let A be the event of aliens sending signals and R be the event that the signals are received. If the equipment detects signals, the probability that aliens are actually sending them is:

P (A ∣ R) = \frac{P (A) P (R ∣ A)}{P (A) P (R ∣ A) + P (A^{'}) P (R ∣ A^{'})} = \frac{\frac{2}{5} \frac{3}{5}}{\frac{2}{5} \frac{3}{5} + \frac{3}{5} + \frac{1}{10}} = \frac{4}{5}

This is helpful 16

Relevant Questions

asked 2021-03-08

${(x^{4} y^{5})}^{\frac{1}{4}} {(x^{8} y^{5})}^{\frac{1}{5}} = x^{\frac{j}{5}} y^{\frac{k}{4}}$
In the equation above, j and k are constants. If the equation is true for all positive real values of x and y, what is the value of $j - k$ ?
A)3
B)4
C)5
D)6

See answers (1)

asked 2021-08-16

Classify each of the studies as either descriptive or inferential. Explain your answers. In an article titled “Teaching and Assessing Information Literacy in a Geography Program” (Journal of Geography, Vol. 104, No. 1, pp. 17-23), Dr. M. Kimsey and S. Lynn Cameron reported results from an on-line assessment instrument given to senior geography students at one institution of higher learning. The results for level of performance of 22 senior geography majors in 2003 and 29 senior geography majors in 2004 are presented in the following table. Level of performance Met the standard: 36−48 items correct Passed at the advanced level: 41−48 items correct Failed: 0−35 items correct Percent in 2003 82%50%18% Percent in 2004 93%59%7% Level of performance Met the standard: 36−48 items correct
Passed at the advanced level: 41−48 items correct
Failed: 0−35 items correct
Percent in 2003
82%
50%
18%
Percent in 2004
93%
59%
7%

See answers (1)

asked 2021-01-31

The function W defined by

W (α) = 1.9 α + 2.3

models the weight of a kitten, in ounces, that is a weeks old for

0 \leq α \leq 6

. According to this model, what is the weight, in ounces, of a kitten that is 3 weeks old?

See answers (1)

asked 2022-05-09

Identify each of the following statements as true or false in relation to confidence intervals (CIs).
Note: 0.5 marks will be taken away for each incorrect answer. The minimum score is 0.

	True	False
A 95% CI is a numerical interval within which we are 95% confident that the true mean μ $μ$ lies.
A 95% CI is a numerical interval within which we are 95% confident that the sample mean x¯¯¯ $\bar{x}$ lies.
The true mean μ $μ$ is always inside the corresponding confidence interval.
For a sample size n=29 $n = 29$ , the number of degrees of freedom is n=30 $n = 30$ .
If we repeat an experiment 100 times (with 100 different samples) and construct a 95% CI each time, then approximately 5 of those 100 CIs would not $n o t$ contain the true mean 𝜇.