If p(a|b) = 0.35, p(b) = 0.75 and p(a) = 0.44 are the events a and b independent ?

1 answer:

6 0

Hello :
note 1 :
p(A|B) = p(A∩B)/ p(B)

note 2 :
 A and B independent: p(A∩B) = p(A)×p(B)
calculate : p(A∩B)
p(A∩B) = p(A|B)×p(B)
p(A∩B) = 0.35 ×0.75 = 0.2625
but : p(A)×p(B) = 0.44×0.75 = 0.33
conclusion :
the events A and B are not independent ?

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From a July 2019 survey of 1186 randomly selected Americans ages 18-29, it was discovered that 248 of them vaped (used an e-ciga

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Answer:

The 90% confidence interval is (0.1897, 0.2285).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

For this problem, we have that:

From a July 2019 survey of 1186 randomly selected Americans ages 18-29, it was discovered that 248 of them vaped (used an e-cigarette) in the past week. This means that $n = 1186, \pi = \frac{248}{1186} = 0.2091$