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2 answers:
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Answer: a) Independent
b) Independent
c) Dependent
Step-by-step explanation:
Since, If a coin is tossed three times,
Then, total number of outcomes, n(S) = 8
a) : tails comes up with the coin is tossed the first time;
= { TTT, THH, THT, TTH }
: heads comes up when the coin is tossed the second time.
= { THT, HHH, THH, HHT }
Thus,
⇒
Similarly,
⇒
Since, = { THH, THT }
⇒
Thus,
Therefore, and
are independent events.
B) : the first coin comes up tails
= { TTT, THH, THT, TTH }
: two, and not three, heads come up in a row
= { HHT, THH }
Thus,
⇒
Similarly,
⇒
Since, = { THH }
⇒
Thus,
Therefore, and
are independent events.
C) : the second coin comes up tails;
= { HTH, HTT, TTT, TTH }
: two, and not three, heads come up in a row
= { HHT, THH }
Thus,
⇒
Similarly,
⇒
Since, =
⇒
Thus,
Therefore, and
are dependent events.