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Anestetic [448]
3 years ago
12

Geoff has a bag that contains 4 red marbles and 6 blue marbles. He chooses two marbles at random and does not replace them. What

is the probability that the first marble is blue and the second marble is red? A. B. C. D.
Mathematics
1 answer:
posledela3 years ago
3 0

Total number of marbles = 10

Number of red marbles = 4

Number of blue marbles = 6

Probability = \frac{number of favorable outcomes}{total number of outcomes}

The probability that the first marble is blue = \frac{6}{10}

The probability that the first marble is red = \frac{4}{9} ; 9 because 1 marble has already been taken out.

Joint probability= probability of event A * Probability of event B

= \frac{6}{10}\times\frac{4}{9}=\frac{24}{90}= \frac{4}{15}

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3 years ago
The heights (measured in inches) of men aged 20 to 29 follow approximately the normal distribution with mean 69.3 and standard d
Zolol [24]

Answer:

The middle 92% of all heights fall between 64.4 inches and 74.2 inches.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

In this problem, we have that:

\mu = 69.3, \sigma = 2.8

Between what two values does that middle 92% of all heights fall?

The middle 92% falls from X when Z has a pvalue of 0.5 - 0.92/2 = 0.04 to X when Z has a pvalue of 0.5 + 0.92/2 = 0.96. So from the 4th percentile to the 96th percentile.

4th percentile

X when Z = -1.75

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

-1.75 = \frac{X - 69.3}{2.8}

X - 69.3 = -1.75*2.8

X = 64.4

96th percentile

X when Z = 1.75

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

1.75 = \frac{X - 69.3}{2.8}

X - 69.3 = 1.75*2.8

X = 74.2

The middle 92% of all heights fall between 64.4 inches and 74.2 inches.

6 0
3 years ago
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