Part A. You have a fair coin. You flip the coin two times. Let 7, the the event
ID: 3310741 • Letter: P
Question
Part A. You have a fair coin. You flip the coin two times. Let 7, the the event that the first fipFlip 1) results in Tails. Let T2 be the event that the second flip (Pip 2) results in Tails. Are the events T and T2 independent? Cho09e... Which one of the following calculations would Bllow you to make this conclusion? Choose.... (a) Comparing p(T2 n Ti) against p(T2) Comparing p(T2 l T, ) against p(T) (c) Comparing p(T2) against p(T) (a)Comparing P(T2 |T) against p(Ti |T) For Parts B and C, consider the following scenario, Suppose now that you have three coins in your pocket. Two of the coins are fair, but the third coin has tais on both sides. You reach into your pocket withcut looking, pull out a coin, and you flip this coin two times Part B. Without any knowledge of the reeult of the first flp, what is the probability of getting Tails on the second flip? That is, what is p(T2)? If you observe that the reeult of the firet flip is Talls, what is the probability that the second fip will also result in Tails? Are the events Ti and T'z independent? Choose Part C For Part C only, suppose that before you flip the coin, you observe that it is a fair coin (call this event F) Given this information, yau would calculate that the probabilty of the second flip resuting in Tails is p(T Fand you would also calculate that the probabilty of the second fip resuiting in Tails given that the first flip resulted in Tails is PTF 122 Which one of the tollowing can you conclude about Ti and T2? Choos...Explanation / Answer
Part A.
Event T1 and T2 are independent - Yes
Because tossing a coin two times are independent events
This can be concluded after comparing P(T2|T1) against P(T1|T2)
Part B.
Probability of getting tail on second flip, P(T2) = 0.5
If first flip results into tail, probability that second flip also results into tail, 0.5
Event T1 and T2 are independent - Yes