Answer the following questions showing all work. Full credit will not be given t

Question

Answer the following questions showing all work. Full credit will not be given to answers without work shown. If you use Minitab Express include the appropriate output (copy + paste) along with an explanation. Output without explanation will not receive full credit. Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board.

2. [24 points] You are going to need a coin to complete this question, any coin with a heads side and a tails side will work.

A. You are going to flip the coin three times. Explain why these three coin flips are independent trials.

B. If a fair coin in flipped three times, what is the probability of flipping heads twice and tails once?

C. Flip your coin three times. What were your results?

D. If you were to flip your coin again three times, what is the probability that you would obtain the same results as you did in part C in the same order?

Explanation / Answer

(A) Trials are called independent if the probability of outcome of one trial is not affected by the outcome of the other. In this case getting head or tail in first trial, its probability is 1/2.
In second trial its probability remains unaffected i.e. 1/2 though the outcome in first is either head or tail.

Hence these trails are independent.

(B)
Probabiltiy of getting head/tail when a coin is flipped is 1/2. P(H) = 1/2 and P(T) = 1/2

Probability of getting head twice is 3C2 * (1/2)^2 * (1/2) = 3/8

(C)
Result of flipping a coin thrice is Head, Tail and Head

(D)
Possible outcomes when a coin is flipped thice are {(HHH), (TTT), (HTH), (HHT), (THH), (THT), (TTH), (HTT)} i.e. 8 outcomes.

probability of getting same outcome is 1/8

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