Statistics and Probability Answers

For the given pair of events, classify the two events as independent or dependent. (If two events are technically dependent but can be treated as if they are independents according to the 5% guideline, consider them to be independent.)
Randomly selecting a city in Texas
Randomly selecting a county in Texas
A. The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other.
B. The two events are independent because the occurrence of one affects the probability of the occurrence of the other.
C. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
D. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.

In a package of M&Ms there are 20 pieces. The pieces come in 6 different colors: red, blue, green, yellow, orange and brown. Assuming that the M&M colors occur with equal probability, what is the probability of getting 5 green M&Ms in a package, using binomial distribution.

The probability that it will rain on any given day in the month of June is .02. What is the probability that it will rain once in the month of June?

The probability that I go to the gym on any given day of the week is 30%.
What is the probability distribution of the number of times that I go to the gym over the course of one week (7 days).

My physician recommends that I go to the gym at least 3 times per week. What is the probability that I follow the physician’s recommendation and go to the gym at least 3 times in a one week period?

70% of disk drives made from Comdrive function properly. If we have a collection of 5 disk drives what is the probability that:

a) At least one disk drive doesn’t function?
b) At least one disk drive is functioning

You roll a fair 6-sided die 8 times. What is the probability that you will roll at least four “4’s”?

Thanks in advance.

a sample of 400 students of undergraduate and 400 students of post graduate classes were taken to know their opinion about autonomous college. 290 of the undergraduate and 310 of the post graduate students favoured the autonomous status. Present these fact in the form of a table and test at 5% level, that the opinion regarding autonomous status of college are independent of the level of classes of students.

Of the Type A electrical resistors produced by a factory, 85% have
resistance greater than 41 ohms, and 3.7% of them have resistance
greater than 45 ohms. The resistances follow a normal distribution.
What percentage of these resistors have resistance greater than 44
ohms?

Experiment - choosing two cards with replacement from a standard deck of cards
Event A - the first card is a seven
Event B - the second card is a seven
Is this independent or dependent

35 ribbons in a drawer. 7 yellow 6 blue 9 red 3 green each ribbon selected only once. what is probability 2 green ribbons will be selected