Please can somebody help me with this

A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm sounds with probability 0.95. When

Lapatulllka [165]

Answer:

6.56% probability that a real emergency situation exists.

Step-by-step explanation:

We have these following probabilities:

A 0.4% probability that a real emergency situation exists.

A 99.6% probability that a real emergency situation does not exist.

If an emergency situation exists, a 95% probability that the alarm sounds.

If an emergency situation does not exist, a 2% probability that the alarm sounds.

The problem can be formulated as the following question:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

In this problem:

What is the probability of a real emergency situation existing, given that the alarm has sounded.

P(B) is the probability of there being a real emergency situation. So $P(B) = 0.004$ .

P(A/B) is the probability of the alarm sounding when there is a real emergency situation. So P(A/B) = 0.95.

P(A) is the probability of the alarm sounding. This is 95% of 0.4%(real emergency situation) and 2% of 99.6%(no real emergency situation). So

P(A) = 0.95*0.04 + 0.02*0.996 = 0.05792

Given that the alarm has just sounded, what is the probability that a real emergency situation exists?

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.004*0.95}{0.05792} = 0.0656$

6.56% probability that a real emergency situation exists.

6 0

3 years ago

Let's say that 1/3 of the eggs become cracked. What is the ratio of the number of eggs that have cracked to the number of eggs t

vladimir2022 [97]

We can say we have 2 cracked egss and 4 uncracked eggs for a 6 egg total.

The ratio of cracked to uncracked eggs is 2:4 which reduces to 1 to 2.

6 0

3 years ago

Rewrite 256 in exponential form using 2 as the base

AlexFokin [52]

256=2^8
256 is 2^8
I hate this " at least 20 characters to explain" may be the answer doesn't need to be explained so much

5 0

3 years ago

laura walks3_5mile to school each day. lsaiahs walk to school is 3 times as long as lauras.how far does lsaiah walk to school ea

ahrayia [7]

In this question, it is important to understand the words of the problem and then note down the details already provided in the problem. This will make the solving of this problem easier.Now coming to the details already given.

Distance walked by Laura to reach school each day = 3/5 mile

Distance walked by Isaiah to reach school is 3 times that of Laura and it is already given in the question.

Then

The distance walked by Isaiah to reach school each day = (3/5) * 3

= 9/5

= 1 4/5

So Isaiah walks a distance of 1 4/5 miles each day for reaching school. I hope that the procedure of doing such problems is clear to you and yiou can attempt such problems in future without needing any help.

Hope this helps!

6 0

3 years ago

I WILL GIVE BRAINLIEST TO THE FIRST ONE RIGHT!

MArishka [77]

Answer:

E = 15 +16 = 31

6 males like cats ( the middle section) so C = 6

d = 6 +16 = 22

a = 19-6 = 13

b = 50-22 = 28

so in order: a = 13, b = 28, c = 6, d = 22, e = 31

Step-by-step explanation:

3 0

3 years ago

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