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tamaranim1 [39]
3 years ago
14

A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. Two marbles are chosen from

the bag. What expression would give the probability that one marble is yellow and the other marble is red? P(Y and R) = P(Y and R) = P(Y and R) = P(Y and R) = -----We Have Reached 50 Thanks!!! The 50pts Question Will Be Up Tomorrow Around 8:00am - 10:00am Stay Toon!!!!!!!!!!
Mathematics
2 answers:
Kryger [21]3 years ago
8 0

Answer:

The expression would give the probability that one marble is yellow and the other marble is red is,

P(Y\cdot R\ And\ R\cdot Y)=P(Y)P(R)+P(R)P(Y)

Step-by-step explanation:

A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. So in total there are 25 marbles.

Hence,

Probability of getting yellow ball = P(Y)=\dfrac{8}{25}

Probability of getting red ball = P(R)=\dfrac{5}{25}

Probability that one marble is yellow and the other marble is red is,

P(Y\cdot R\ And\ R\cdot Y)=P(Y)P(R)+P(R)P(Y)=\dfrac{8}{25}\cdot \dfrac{5}{25}+\dfrac{5}{25}\cdot \dfrac{8}{25}=0.128

elena-14-01-66 [18.8K]3 years ago
7 0
Y and r: 0.04 or 4% ---------------------

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Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and
WINSTONCH [101]

Answer:

n=170

Step-by-step explanation:

1) Notation and definitions

n random sample taken (variable of interest)

\hat p=0.65 estimated proportion.

p true population

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".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by \alpha=1-0.90=0.1 and \alpha/2 =0.05. And the critical value would be given by:

z_{\alpha/2}=\pm 1.64

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.06 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.65(1-0.65)}{(\frac{0.06}{1.64})^2}=169.968  

And rounded up we have that n=170

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The interest she would pay is $694.40.

<h3>What is simple interest?</h3>

Simple interest rate is the interest that is paid only on the principal portion of a loan. This means that the debtor does not pays interest on the interest rate already accrued.

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