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swat32
2 years ago
5

4 green marbles, 5 red marbles, and 2 yellow marbles are placed into a bag. One marble is chosen and replaced into the bag. A se

cond marble is chosen. What is the probability a red marble and then a yellow marble are chosen? Write answer in simplest fraction form,
Mathematics
1 answer:
Ipatiy [6.2K]2 years ago
7 0

Answer:

The probability is 10/121

Step-by-step explanation:

In this question, we are tasked with calculating probability.

The probability to be calculated is that we have an ordered selection of picking a red marble after which we pick a yellow marble.

Firstly let us know the total number of marbles we have. That will be 4 + 5 + 2 = 11 marbles

Probability of picking a red marble will be 5/11 while the probability of picking a yellow marble will be 2/11

Now, the probability of picking a red marble before a yellow marble will be mathematically equal to; P(r) * P(y) = 5/11 * 2/11 = 10/121

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Answer is C because it's less than.

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3 years ago
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There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters tha
uranmaximum [27]

Answer:

0.6826 = 68.26% probability that the first machine produces an acceptable cork.

0.933 = 93.3% probability that the second machine produces an acceptable cork.

The second machine is more likely to produce an acceptable cork.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

What is the probability that the first machine produces an acceptable cork?

The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.10 cm, which means that \mu = 3, \sigma = 0.1

Acceptable between 2.9 and 3.1, which means that this probability is the pvalue of Z when X = 3.1 subtracted by the pvalue of Z when X = 2.9.

X = 3.1

Z = \frac{X - \mu}{\sigma}

Z = \frac{3.1 - 3}{0.1}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 2.9

Z = \frac{X - \mu}{\sigma}

Z = \frac{2.9 - 3}{0.1}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826 = 68.26% probability that the first machine produces an acceptable cork.

What is the probability that the second machine produces an acceptable cork? (Round your answer to four decimal places.)

For the second machine, we have that \mu = 3.04, \sigma = 0.04. Same probability we have to find out. So

X = 3.1

Z = \frac{X - \mu}{\sigma}

Z = \frac{3.1 - 3.04}{0.04}

Z = 1.5

Z = 1.5 has a pvalue of 0.9332

X = 2.9

Z = \frac{X - \mu}{\sigma}

Z = \frac{2.9 - 3.04}{0.04}

Z = -3.5

Z = -3.5 has a pvalue of 0.0002

0.9332 - 0.0002 = 0.933

0.933 = 93.3% probability that the second machine produces an acceptable cork.

Which machine is more likely to produce an acceptable cork?

Second one has a higer probability, so it is more likely to produce an acceptable cork.

6 0
3 years ago
Natsumi opens a savings account that earns 0.08% interest on the last day of the month. Her initial deposit is $75 on the first
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Because she doesn't receive any interest on the last month, but puts money in, we can write this equation:

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Step 2: Divide both sides by -3.

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mrs_skeptik [129]
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<span>See the attached figure for the detailed solution.
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