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2 years ago

12

What is the value of x

1 answer:

Elenna [48]2 years ago

4 0

Answer:

The value of X is 4 and the value of Y is 3

Step-by-step explanation:

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There are three power plants [X, Y, Z] that at any given time each one either generates electricity or idles. Event A is that pl

insens350 [35]

We're told that

$P(A\cap B)=0.15$

$P(A\cup B)^C=0.06\implies P(A\cup B)=0.94$

$P(B\mid A)=P(B^C\mid A)=0.5$

where the last fact is due to the law of total probability:

$P(A)=P(A\cap B)+P(A\cap B^C)$

$\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)$

$\implies 1=P(B\mid A)+P(B^C\mid A)$

so that $B\mid A$ and $B^C\mid A$ are complementary.

By definition of conditional probability, we have

$P(B\mid A)=P(B^C\mid A)$

$\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}$

$\implies P(A\cap B)=P(A\cap B^C)$

We make use of the addition rule and complementary probabilities to rewrite this as

$P(A\cap B)=P(A\cap B^C)$

$\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)$

$\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)$

$\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]$

$\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]$

$\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C$

$\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)$

By the law of total probability,

$P(B)=P(A\cap B)+P(A^C\cap B)$

$\implies P(A^C\cap B)=P(B)-P(A\cap B)$

and substituting this into $(*)$ gives

$2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]$

$\implies P(B)=P(A\cup B)-P(A\cap B)$

$\implies P(B)=0.94-0.15=\boxed{0.79}$

8 0

2 years ago

The Rodriguez family went to the movies on Friday night. At AMC, adult tickets are $13 and children tickets are $7. The family o

morpeh [17]

X+y=6
13x+7y=54
solve the system for x,y

4 0

3 years ago

I've literally asked this question 5 times lol. Can someone please help me?

Tju [1.3M]

I think i know the answer to that question. just wait for a sec.

6 0

2 years ago

Read 2 more answers

The local Beep Boop store sells widgets and gizmos. If you subtract the cost of 3 gizmos from 7 widgets you would spend 28 Boop

jasenka [17]

Answer:

$7

Step-by-step explanation:

8 0

2 years ago

1 tree makes approximately 230 newspapers. Estimate (by rounding each number to 1 S.F.) how many newspapers 56 trees will make.

g100num [7]

Answer:

56 trees will make 10000 newspapers.

Step-by-step explanation:

Given:

One tree makes approximately 230 newspapers.

Now, for estimating how many newspapers will be made with 56 trees.

By multiplying $56$ trees with $230$ newspapers we get,

$56\times230=12880$ .

And, rounding $12880$ to one significant number (1 S.F.) is $10000$ .

Therefore, 56 trees will make 10000 newspapers.

6 0

3 years ago

Read 2 more answers