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Xelga [282]
2 years ago
12

You have a bag which contains 15 slips of paper that are num- bered 1 through 15. You pull a piece of paper from the bag, do not

return it, and then pull another piece of paper from the bag. What is the probability that both slips of paper you pull are out are a multiple of 4? Express your answer as a fully simplified fraction.
Mathematics
1 answer:
BARSIC [14]2 years ago
3 0

Answer:

<u>The correct answer is 1/35 (fully simplified fraction)</u>

Step-by-step explanation:

Number of slips of paper in the bag = 15

Number of slips of paper in the bag that are a multiple of 4 = 3 (those numbered 4, 8 and 12)

Using Laplace Rule, that states that the probability of an event X is obtained by dividing the number of results that form event X by the number of possible outcomes, provided that the elementary events are equiprobable, that is, that all possible outcomes have the same probability.

Probability of pulling a 1st piece of paper multiple of 4 = 3/15 = 1/5

Now we have a second event Y that is not independent from the first event X, because now the number of slips is 14 and not 15, you're not returning the first slip of paper.

Probability of pulling a 2nd piece of paper multiple of 4 = Probability of the 1st event * probability of the 2nd event after it happened the 1st one

Probability of pulling a 2nd piece of paper multiple of 4 = 1/5 * 2/14

Probability of pulling a 2nd piece of paper multiple of 4 = 2/70 = 1/35

<u>The probability of pulling two slips of paper both numbered with a multiple of 4 is 1/35.</u>

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Step-by-step explanation:

Let the numbers be x and y

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x - y + 2 = 0

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x = 48

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= 48 +2

= 50

Therefore the 2 nos. are 48 and 50

Hope this answers helps you

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3 years ago
Which set of ordered pairs represents a function?
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The one that doesn't have an "x" repeated, that is an X-REPEAT
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6 0
3 years ago
Read 2 more answers
A certain store sells small, medium and large toy trucks in each of the colors red blue green and yellow. the store has an equal
tangare [24]
There is a 1/2 chance that he will get at least one of the two features.

There are 3 x 4 = 12 possibilities. There are all 4 colors of each 3 sizes.

All 4 of the medium trucks have one of the features.

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3 0
3 years ago
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A maker of a certain brand of low-fat cereal barsclaims that the average saturated fat content is 0.5gram. In a random sample of
finlep [7]

Answer:

t=\frac{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386    

p_v =2*P(t_{(7)}  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance.  So then the claim makes sense

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

In order to calculate the mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}} (3)  

The mean calculated for this case is \bar X=0.475

The sample deviation calculated s=0.183

We need to conduct a hypothesis in order to check if the true mean is 0.5 or no, the system of hypothesis would be:  

Null hypothesis:\mu = 0.5  

Alternative hypothesis:\mu \neq 0.5  

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{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=8-1=7  

Since is a two sided test the p value would be:  

p_v =2*P(t_{(7)}  

Conclusion  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance.  So then the claim makes sense

4 0
3 years ago
Read 2 more answers
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