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jolli1 [7]
3 years ago
9

A commuter crosses one of three bridges, A, B, or C, to go home from work. The commuter crosses bridge A with probability 1/3, c

rosses bridge B with probability 1/6, and crosses bridge C with probability 1/2. The commuter arrives home by 6pm with probability 75%, 60%, and 80% by crossing bridge A, B, or C, respectively. If the commuter arrives home by 6pm, find the probability that bridge B was used.
Mathematics
1 answer:
mihalych1998 [28]3 years ago
8 0

Answer:

0.1333 = 13.33% probability that bridge B was used.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Arrives home by 6 pm

Event B: Bridge B used.

Probability of arriving home by 6 pm:

75% of 1/3(Bridge A)

60% of 1/6(Bridge B)

80% of 1/2(Bridge C)

So

P(A) = 0.75*\frac{1}{3} + 0.6*\frac{1}{6} + 0.8*\frac{1}{2} = 0.75

Probability of arriving home by 6 pm using Bridge B:

60% of 1/6. So

P(A \cap B) = 0.6*\frac{1}{6} = 0.1

Find the probability that bridge B was used.

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1}{0.75} = 0.1333

0.1333 = 13.33% probability that bridge B was used.

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Lexie worked for 5 hours and 30 minutes. How should she write it on her time card? A. 5.25 B. 5.3 C. 5.5 D. 5.75
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An analyst from an energy research institute in California wishes to precisely estimate a 99% confidence interval of the average
Lena [83]

Answer:

190

Step-by-step explanation:

Data provided in the question:

Confidence level = 99%

Therefore,

α = 1% = 0.01

[ from standard normal table ]

z-value for z_{\frac{\alpha}{2}}= z_{\frac{0.01}{2}}= = 2.58

Margin of error, E = $0.06

Standard deviation, σ = $0.32

Now,

n = (\frac{z_{0.005}\sigma}{E})^2

Here,

n is the sample size (or the minimum number of gas stations  )

on substituting the respective values, we get

= (\frac{z_{0.005}\sigma}{E})^2

= (\frac{2.58\times0.32}{0.06})^2

= 13.76²

= 189.3376 ≈ 190

Hence,

minimum number of gas stations that she should include in her sample is 190

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State the domain restriction(s) in interval notation of \displaystyle f\left(g\left(x\right)\right)f(g(x)) given: \displaystyle
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Answer:

The interval notation for the domain is [\frac{23}{3},\infty  ].

Step-by-step explanation:

Consider the provided information.

It is given that \:f\left(x\right)=\sqrt{3x-2},\:\text{ and }\:g\left(x\right)=x-7

We need to find the value of f\left(g\left(x\right)\right).

Put the value of g(x) in  f\left(g\left(x\right)\right).

f\left(g\left(x\right)\right)=f(x-7)  ....(1)

Now, put x=x-7 in \:f\left(x\right)=\sqrt{3x-2}

\:f\left(x-7\right)= \sqrt{3(x-7)-2}

\:f\left(x-7\right)= \sqrt{3x-21-2}

\:f\left(x-7\right)= \sqrt{3x-23}

From equation 1.

f\left(g\left(x\right)\right)=\:f\left(x-7\right)= \sqrt{3x-23}

The domain of the function is the set of input values for which a function is defined.

Here, the value of 3x-23 should be greater or equal to 0 as the square root of a negative number is not real.

Domain= 3x-23\geq0

x\geq\frac{23}{3}

The value of x is all real number greater than \frac{23}{3}.

Hence, the interval notation for the domain is [\frac{23}{3},\infty  ].

7 0
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