Suppose that we want to generate a random variable X that is equally likely to be either 0 or 1, and that all we have at our disposal is a biased coin that, when flipped, lands on heads with some (unknown) probability p. Consider the following procedure: 1. Flip the coin, and let 21, either heads or tails, be the result.
2. Flip the coin again, and let Z2 be the result.
3. If Z and Z, are the same, return to step 1.
4. If Z, is heads, set X = 0, otherwise set X = 1.
a) Let I, and I be independent indicator variables with success probability p. Compute P(11 = 1|11 # 12)
b) Show that the random variable X generated by this procedure is equally likely to be either 0 or 1.
c) Could we use a simpler procedure that continues to flip the coin until the last two flips are different, and then sets X = 0 if the final flip is a head, and sets X = 1 if it is a tail?
PROBLEM 4.7
Implement the algorithm described in the previous problem in R and use it to generate 10 standard uniformly distributed variables.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

it’s the first one your welcome

80x^8−68x^6+16^5−20x^4−4x^3+8x^2

hope i'm right lol

total of apples - take away four

6-4 = 2

answer is 2 apples