Suppose at the shooting range you have a probability of hitting the bullseye on your target of about 10%.

A) What is the probability of hitting the bullseye more than 1 time in 20 shots?

B) What is the mean number of bullseye's you would expect in 20 shots?

C) What is the Standard Deviation of bullseye's you would expect in 20 shots?

PROBLEM 2. 20 pts. An urn contains 4 Red balls and 6 Green balls. If 4 balls are taken one at a time with replacement. Find the probability that one is R. Find also the expected number of R and the standard deviation of R If 4 two balls are taken one at a time without replacement. Find the probability that only one is Red

PROBLEM 2.  20 pts.  An urn contains 4 Red balls and 6 Green balls.

1. If 4 balls are taken one at a time with replacement. Find the probability that one is R. Find also the expected number of R and the standard deviation of R
2. If 4 two balls are taken one at a time without replacement. Find the probability that only one is Red

According to a government study, 8% of all children live in a household that has an income below the poverty level. If a random sample of 20 children is selected:

a) what is the probability that 5 or more live in poverty?

b) what is the probability that 4 live in poverty?

c) what is the expected number (mean) that live in poverty? What is the variance? What is the standard deviation?

The number 73 is written as a sum of three natural numbers

73=a+b+c

(the triple (a,b,c) is ordered; e.g., the decompositions 73=19+20+34 and 73=20+34+19 are different.
Also, assume that all the decompositions have equal probability.)
Given that there exists a triangle with sides a, b, and c, what is the probability that this triangle is isosceles?

3. John is proofreading his own essay. From the past experience, he knows that the probability that any page contains at least one typo is equal to 0.7. The essay he is reading now is 20 pages long. What is the probability that this essay has no more than 15 typos? Assume Poisson distribution of the typos number in John’s essays.

A box contains 7 red and 5 blue marbles. Suppose we select one marble at a time with
replacement.
a. Determine the probability that the first blue marble appears on the fourth selection.
b. Determine the probability that out of the first 10 selection, there are at least 2 red
marbles.
c. For part (b), determine the expected and variance number of red marbles selected.

You have two coins, one of which you know to be fair and the other of which has a probability of turning up heads of 0.7, but you can’t tell which one is which. You choose one coin at random and flip it ten times getting an equal number of heads and tails. What is the probability that you chose the unfair coin?

Is there a way to do this without the binomial probability?

Consider the following game: You roll six 6-sided dice d1,…,d6 and you win if some number appears 3 or more times. For example, if you roll:

(3,3,5,4,6,6)

then you lose. If you roll

(4,1,3,6,4,4)then you win.

What is the probability that you win this game?

The answer is 119/324