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amm1812
2 years ago
13

In London, half of the days have some rain. The weather forecaster is correct 2/3 of thetime, i.e., the probability that it rain

s, given that she has predicted rain, and the probabilitythat it does not rain, given that she has predicted that it won’t rain, are both equal to 2/3.When rain is forecast, Mr. Pickwick takes his umbrella. When rain is not forecast, he takesit with probability 1/3. Find (a) the probability that Pickwick has no umbrella, given that itrains. (b) the probability that it doesn’t rain, given that he brings his umbrella.
Mathematics
2 answers:
Tema [17]2 years ago
7 0

Answer:

The other person is right

Step-by-step explanation:

Mnenie [13.5K]2 years ago
3 0

Answer:

(a) The probability that Pickwick has no umbrella, given that it rains is 2/9

(b) The probability that it doesn’t rain, given that he brings his umbrella is 5/9

Step-by-step explanation:

(a) The probability that Pickwick has no umbrella, given that it rains: P1

P1 = P (rain) * P (not umbrella)

This probability have two components, if rain forecasts or not rain forecasts:

  1. When rain is forecast Mr. Pickwick takes his umbrella, so the probability of not umbrella is zero and the probability of rain for a rain forecast is 2/3 (the weather forecaster is correct 2/3 of the time)
  2. When not rain forecast, he takes it with probability 1/3, so the probability of not takes it is 2/3 and the probability of rain with a not rain forecast is 1/3 (the weather forecaster is correct 2/3 of the time, so there is 1/3 probability of rain)

P1 = 2/3*0 + 1/3*2/3 = 0 + 2/9 = 2/9

The probability that Pickwick has no umbrella, given that it rains is 2/9

(b) The probability that it doesn’t rain, given that he brings his umbrella: P2

P2 = P (not rain) * P (umbrella)

This probability have two components, if rain forecasts or not rain forecasts:

  1. When rain is forecast Mr. Pickwick takes his umbrella, so the probability is one and the probability of rain for a rain forecast is 2/3, so the probability of rain is 1/3  (the weather forecaster is correct 2/3 of the time, so 1/3 will be wrong)
  2. When not rain forecast, he takes it with probability 1/3 and the probability of not rain with a not rain forecast is 2/3 (the weather forecaster is correct 2/3 of the time)

P1 = 1/3*1 + 2/3*1/3 = 1/3 + 2/9 = 5/9

The probability that it doesn’t rain, given that he brings his umbrella is 5/9

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Step-by-step explanation:

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A=(1,3,5.7,9) <br>B= (2,4,6,8,10)<br>C= (1,5,6,7,9)<br>A intersects (B intersects C)=
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8 0
3 years ago
Read 2 more answers
The mean waiting time at a drive-through of a fast-food restaurant from the time the order is received is 84 seconds. A manager
olga nikolaevna [1]

Answer:

t=\frac{81-84}{\frac{3.6}{\sqrt{100}}}=-8.33    

And the standard score for this case is -8.33

Step-by-step explanation:

Data given and notation  

\bar X=81 represent the sample mean

s=3.6 represent the sample standard deviation

n=100 sample size  

\mu_o =84 represent the value that we want to test

\alpha=0.05 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the ture mean is lower than 84, the system of hypothesis would be:  

Null hypothesis:\mu \geq 84  

Alternative hypothesis:\mu < 84  

If we analyze the size for the sample is > 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{81-84}{\frac{3.6}{\sqrt{100}}}=-8.33    

And the standard score for this case is -8.33

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2 years ago
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mamaluj [8]

Answer:

x=-1/6

Step-by-step explanation:

In the attached file

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