Please show ALL work. Incomplete/incorrect answers will receive a THUMBS DOWN wh

Question

Please show ALL work. Incomplete/incorrect answers will receive a THUMBS DOWN while thorough and complete answers will receive a THUMBS UP! Thanks for your help.

(20 pts) A coin is flipped 4 times and the outcome is reported as ci c2 c3 c1, where ci denotes the coin value on the ith coin flip. For example, 'HHTH' suggests that c3 "T', ie., the third coin flip resulted in 'T (a) List all the outcomes of this experiment. (b) Determine whether the events A C1 c2 n C3 c4 and B {c1 c3 n C2 c1h are mutually exclusive. (c) Determine whether the events A C1 c2 n C3 c4 and B {c1 c3 n C2 c1h are statistically independent.

Explanation / Answer

a)
Write down ALL of the possible results for flipping a coin 4 times;
there are 16 patterns.

hhhh
--------
hhht
hhth
hthh
thhh
tthh
thth
thht
htht
hhtt
htth

thtt
ttht
ttth

b) from above outcomes

  Mutually exclusive events cannot happen at the same time. For example: when tossing a coin, the result can either be heads or tails but cannot be both

BUT HERE two mutually exclusive events=event of A CONTAINS SOME EVENTS IN B

C)Implicitly, we are relying on the assumption that each coin flip is independent. When coin flips areindependent, it means that the probability of a coin coming up heads does not depend in any way on previous coin flips''

HERE TWO SETS ARE INDEPENDENT IF ONLY DOEST HAVE ANY COMMON DATA

but here we have... so,they are not independent

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