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givi [52]
3 years ago
5

Consider the following portion of an electric circuit with three relays. Current will flow from point a to point b if there is a

t least one closed path when the relays are activated. The relays may malfunction and not close when activated. Suppose that the relays act independently of one another and close properly when activated, with a probability of .9. Given that current flowed when the relays were activated, what is the probability that relay 1 functioned?
Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
4 0

Answer:

0.9009

Step-by-step explanation:

Let X be the event that Current will flow

Let Y be the event that the first relay which is 1 is closed

Thus, we can say that every element of Y is in X, but X possesses more elements. Thus, Y ⊂ X.

Thus, we can say that;

P(X ∩ Y) = P(Y)

Thus, given that current flowed, the probability that relay 1 functioned will be expressed as;

P(Y | X) = (P(Y ∩ X))/P(X)

From earlier, we saw that P(X ∩ Y) = P(Y). Thus;

P(Y | X) = P(Y)/P(X)

From the question, P(Y) = 0.9

Since there are 3 relays, then we have;

P(X) = 1 - 0.1³ = 0.999

Thus;

P(Y | X) = 0.9/0.999

P(Y | X) = 0.9009

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One die is blue and the other die is yellow. Both are rolled. What is the probability of getting the shm of 8?
suter [353]

Answer:

5 /36

Step-by-step explanation:

Sample space :

Number of faces^number of dice = 6^2 = 36

Sum of 8 on a roll of 2 dies :

Probability = required outcome / Total possible outcomes

Required outcome = number of times a sum of 8 is obtained on a roll of 2 dies = 5

Total possible outcomes = sample space = 36

P(obtaining a sum of 8) = 5 /36

8 0
3 years ago
18,18,15,18,18,24,21,21,24,14 which one is mean
julsineya [31]

Answer:19.1

Step-by-step explanation: Put the numbers in order and then add the numbers and then divide it by how many number there is

14+15+18+18+18+18+21+21+24+24=191

191/10=19.1

7 0
2 years ago
Ví dụ 1.5. Một người đi mua hàng 3 lần. Xác suất lần đầu mua được hàng tốt là 0,7.
vodka [1.7K]

Answer:

a) 0.50575,

b) 0.042

Step-by-step explanation:

Example 1.5. A person goes shopping 3 times. The probability of buying a good product for the first time is 0.7.

If the first time you can buy good products, the next time you can buy good products is 0.85;  (I interpret this as, if you buy a good product, then the next time you buy a good product is 0.85).

And if the last time I bought a bad product, the next time I bought a good one is  0.6. Calculate the probability that:

a) All three times the person bought good goods.

P(Good on 1st shopping event AND Good on 2nd shopping event AND Good on 3rd shopping event) =

P(Good on 1st shopping event) *P(Good on 2nd shopping event | Good on 1st shopping event) * P(Good on 3rd shopping event | 1st and 2nd shopping events yield Good) =

(0.7)(0.85)(0.85) =

0.50575      

b) Only the second time that person buys a bad product.

P(Good on 1st shopping event AND Bad on 2nd shopping event AND Good on 3rd shopping event) =

P(Good on 1st shopping event) *P(Bad on 2nd shopping event | Good on 1st shopping event) * P(Good on 3rd shopping event | 1st is Good and 2nd is Bad shopping events) =

(0.7)(1-0.85)(1-0.6) =

(0.7)(0.15)(0.4) =

0.042

5 0
3 years ago
There are 81 red, blue and yellow
wel

Step-by-step explanation:

Here Given

Total counters = 81

red counters are 9 more than the yellow ones.

And Yellow counter = blue counter

So let the Yellow counter be x and as blue counter and yellow counter are same then blue counter will be also x

And by the question

Red counter = 9 + x

Now

9 + x + x + x = 81

9 + 3x = 81

3x = 81 - 9

3x = 72

x = 72 / 3

Therefore x = 24

Now

Red counters = 9 + 24 = 33

Blue counters = 24

Yellow counters = 24

Hope it helped :)

3 0
3 years ago
Read 2 more answers
Patrick wanted to gather data about the cost of joining a community pool in his area. He plotted the data and determined that th
ohaa [14]

Answer:

The y-intercept is 40. This is the cost of registration ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- Patrick wanted to gather data about the cost of joining a community

 pool in his area

- He plotted the data and determined that the average community

 pool membership cost consists of a one-time registration fee and

 a monthly fee

∴ The cost consists of two parts:

# Part A: one-time registration fee, it is a fixed amount not depend on

  any other condition

# Part B: monthly fee, it depends on the number of months

- He modeled that by the equation y = 15 x + 40, where

# y is the cost for the membership

# 15 is the monthly fee

# x is the number of months

# 40 is the one-time registration

- The form of the equation is y = mx + c, where c is the y-intercept

∴ The y-intercept in the equation y = 15 x + 40 is 40

∴ The y-intercept is the one-time registration fee

* The y-intercept is 40. This is the cost of registration

4 0
3 years ago
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