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Mathematics

1 answer:

Anna71 [15]3 years ago

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You draw a card at random from a deck that contains 333 black cards and 777 red cards. What is \text{P(draw a black card})P(draw

enot [183]

Answer:

The probability of picking a black card at random, from a deck with 3 black cards and 7 red ones is 0.3.

Step-by-step explanation:

We will assume that we have 3 black cards and 7 black cards, for a total of 10 cards. Since we are taking one card at random, we can assume that each card is equally likely to be drawn. We have the following event A: The drawn card is a black. We will find the probability of A as counting the number of outcomes that make A to occur and divide it by the total number of possibilities. We are drawing one card, so we have 10 possibilities to be picked. Out of those 10, only 3 cards are black, hence we have 3 possibilites of picking a black card.

Then,

P(A) = 3/10 = 0.3.

6 0

3 years ago

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

Korolek [52]

Answer:

A sample of 499 is needed.

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 level of $1-\alpha$ , 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 $1 - \frac{\alpha}{2}$ .

The margin of error is given by:

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

In this question, we have that:

$\pi = 0.21$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 90% confidence level with an error of at most 0.03

We need a sample of n, which is found when $M = 0.03$ . So