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3 years ago

I’m confused on this one

Mathematics

1 answer:

Murrr4er [49]3 years ago

6 0

This one is a bit confusing without a diagram anyway. We'll assume the typical labeling where A and B are consecutive angles, so the transverse line AB through the parallels makes A and B supplementary:

A + B = 180 degrees

12x + 46 + 7x + 1 = 180

19x = 180 - 47 = 133

x = 133/19 - 7

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Where (nCx) means combinatory and it's given by this formula:

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Step-by-step explanation:

Previous concepts

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Part a

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=16, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The expected value is given by this formula:

$E(X) = np=16*0.2=3.2$

Part b

For this case we want this probability:

$P(X=0)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And using this function we got:

$P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815$

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