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Coin 1 comes up heads with probability .3, whereas coin 2 comes up heads with probability .6. A coin is randomly chosen and flipped 10 times.

(a) Find the probability the first flip lands heads.

(b) Find the expected number of heads in the 10 flips.

(c) Find the probability that there are a total of 7 heads.

Find the probability to randomly assign numbers from 1 to ? to ? people such that exactly two people get the same number (2<?≤?)? Guidance: Start with numbering the people that have the same number and then number the rest.

the US has removed its prior ban on exporting crude oil. what has been the impact of the new policy? what is your position on this issue? who wins? who loses?

A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.04.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 20-year period.

4.) Determine whether the following probability experiment is a binomial experiment. If the probability experiment is not a binomial experiment, state why?

a.) In a town with 400 citizens, 100 randomly selected citizens are asked to identify their religion. The number who identify with a Christian religion is recorded.

b.) An experiment is conducted in which a single die is cast until a 3 comes up. The number of throws required is recorded.

A company prices its tornado insurance using the following assumptions:

• In any calendar year, there can be at most one tornado.

• In any calendar year, the probability of a tornado is 0.01.

• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.

Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 16-year period.

You decide to grow your own tomato plant (A Cosmonaut Yuri to be exact).

Define X to be a random variable denoting how many tomatoes your tomato plant will grow. The probability mass function (pmf) of X is as follows:

Find the probability that you will get four tomatoes.

Find the probability that you will get at least two tomatoes.

Find the probability that you will get less than three tomatoes.

Find the probability that you will get greater than two tomatoes

Find the probability that you will get at most four tomatoes.

Compute the expected number of tomatoes (the expectation X).

Compute the expected value of

Compute the variance of X

Compute the standard deviation of X

Find the probability that the number of tomatoes you will get is less than 5 but greater than 1.

Solve all the following questions from chapter 4 :
1) If a dice is thrown up one time, what is the probability of getting a number greater
than 2 or less than 5 ?
2) If two dice are thrown up once, what is the probability to get total numbers less
than 8 or at most 5 ?
3) If a dice is thrown up one time, what is the probability of getting an odd number
giving that the number is divided by 3 ?
4) If two dice are thrown up once, what is the probability to get total numbers greater
than 11 if the second number is 5 ?
5) If A , B are two events , P(A) = 0.5 , P(B) = 0.2 , P(A and B) = 0.4 , find P(A or B)
6) If A , B are two independent events , P(A) = 0.24 , P(B) = 0.31 , Find P(A or B)
7) If A , B are two events , P(B) = 0.8 , P(A and B) = 0.5 , find P(A \ B)
8) If A , B are two events , P(B) = 0.35 , P(A \ B) = 0.14 , find P(A and B)