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Tanya [424]
2 years ago
7

A driver has three ways to get from one city to another. There is an 80 % chance of encountering atraffic jam given he is on rou

te A , a 60 % chance given he is on route B , and a 30 % chance given he is onroute C. Because of other factors, such as distance and speed limits , the driver uses route A 50 % of thetime and routes B and C each 25 % of the time. If the driver calls the dispatcher to inform him that he isin a traffic jam, find the probability that he selected route A
Mathematics
1 answer:
lukranit [14]2 years ago
4 0

Answer:

The probability is 0.64

Step-by-step explanation:

What we want to calculate here is conditional probability.

Let P(A )= Probability of using route A = 50% = 0.5

Let P( B )= probability of using route B = 25% = 0.25

Let P (C )= probability of using route C = 25% = 0.25

Let T be the probability that he will be in a traffic Jam

The probability that he will be in a traffic Jam if he uses route A = 80%

Mathematically this is written as P( T | A) which is read as probability of T given A

so P( T | A) = 0.8

Same way for B and C which can be written as follows;

P( T | B) = 60% = 0.6

P( T | C) = 30% = 0.3

Now, what do we want to calculate?

He is in a traffic Jam, and we want to find the probability that he used route A. This means we want to find P(A) given T which can be written mathematically as P ( A | T)

We can find this using the other parameters and especially the equation below;

P ( A | T) = P(A) • P( T| A) / {P(A) • P ( T | A) + P(B)• P(T| B) + P(C) • P(T|C)

P( A | T) = (0.5 * 0.8)/ ( 0.5)(0.8) + (0.25)(0.6) + (0.25)(3) = 0.4/(0.4 + 0.75 + 0.075) = 0.4/0.625 = 0.64

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Step-by-step explanation:

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She charges $25 per lawn. This means that the amount charged for x lawns = 25×x = 25x

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2 years ago
Which Is A Correct First Step For Solving This Equation? -5(4x-7)+8=3x
nordsb [41]

I'm not sure if this is a multiple choice question, so I will just solve the equation.

-5 (4x - 7) + 8 = 3x

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1. Distributive Property of Multiplication

(-5)(4x) + (-5)(-7) + 8 = 3x

2. Simplify

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-20x - 27 = 3x

4. Add 27 to both sides and then subtract 3x from both sides to get all the x's by themselves on the same side

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Hope this helps!

5 0
3 years ago
An amount of 41,000 is borrowed for 15 years at 8.5% interest, compounded annually. If the loan is paid in full at the end of th
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Answer: $139390 must be paid back.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = amount to be played back at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount borrowed.

From the information given,

P = 41000

r = 8.5% = 8.5/100 = 0.085

n = 1 because it was compounded once in a year.

t = 15 years

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A = 41000(1 + 0.085)^15

A = 41000(1.085)^15

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Answer:

Step-by-step explanation:

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terms:

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Move all terms containing x to the left, all other terms to the right.  (Remember)

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Combine the like terms again  -5x + 5x = 0

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Then '-6' to each side of the equation.

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