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1 year ago

If P(A)=0.9, P(B)=0.1, and A and B are independent, find P(A and B).

Mathematics

1 answer:

sweet [91]1 year ago

6 0

According to the given statement;

If P(A)=0.9, P(B)=0.1, and A and B are independent, P(A and B)=0.09

<h3>What is probability of event?</h3>

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. Since there are no other possible outcomes and the coin is fair, the odds of both the outcomes, "heads" and "tails," are equally likely to occur. As a result, the probability of either outcome is half.

<u>According to the given value;</u>

P(A) = 0.9

P(B) = 0.1

A and B independent;

We know that independent

P(A∩B) = P(A) · P(B)

= (0.9)*(0.1)

=0.09

P(A∩B) =0.09

hence, If P(A)=0.9, P(B)=0.1, and A and B are independent, P(A and B)=0.09

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We don't know the shape of the distribution, so we use Chebyshev's Theorem to solve this question. It states that:

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So the correct answer is:

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To estimate the mean height μ of male students on your campus,you will measure an SRS of students. You know from government data

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Answer:

a) $\sigma = 0.167$

b) We need a sample of at least 282 young men.

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Problems of normally distributed samples can be 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

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

This Zscore is how many standard deviations the value of the measure X 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.

(a) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have $Z = 3$ and $X - \mu = -0.5$ must have $Z = -3$ .

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

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that $\sigma = 2.8$