Question

Which situation demonstrates the law of large numbers ?

a. if you roll a six-sides number cube 36 times, you will roll a 4 six times.
b. if 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women.
c. if you flip a coin 44 times, you will get heads about 22 times.
d.if it showed four days last month, it will snow four days this month.

The price of three t-shirt styles are $24, $30 and $36. The probability of choosing a $24 t-shirt is 1/6. The probability of choosing a $30 t-shirt is 1/2. The probability of choosing a $36 t-shirt is 1/3. What is the expected value of a t-shirt?

$29
$30
$31
$32

Answer 1

1. If 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women.

2. $31

Explanation:

Got it right on the test.

Answer 2

The law of large numbers in probability, is a theorem that describes the result of performing the same experiment a large number of times because the average of the results obtained from a large number of trials is close enough to the expected value.

So, according to this definition and the situation given , the correct answer is option B - if 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women; because there are larger number of experiment.

Part B:

To get the expected value of a t-shirt we will multiply each of the 3 prices by the associated probability, and then add up these three products-

`(24*(1)/(6))+(30*(1)/(2))+(36*(1)/(3))`

=4 + 15 + 12 = $31

Hence, option C is correct.