A coin is tossed three times. Let A be the ev | vedclass

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(A) The sample space $S$ for tossing a coin three times contains $2^3 = 8$ outcomes: $S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$.Event $A$ (getti

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Dependent events

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(A) The sample space $S$ for tossing a coin three times contains $2^3 = 8$ outcomes: $S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$.Event $A$ (getting three heads) is $\{HHH\}$,so $P(A) = \frac{1}{8}$.Event $B$ (getting a head on the first toss) is $\{HHH, HHT, HTH, HTT\}$,so $P(B) = \frac{4}{8} = \frac{1}{2}$.The intersection $A \cap B$ is $\{HHH\}$,so $P(A \cap B) = \frac{1}{8}$.For events to be independent,we must have $P(A \cap B) = P(A) 	imes P(B)$.Calculating $P(A) 	imes P(B) = \frac{1}{8} 	imes \frac{1}{2} = \frac{1}{16}$.Since $P(A \cap B) = \frac{1}{8} 
eq \frac{1}{16}$,the events are dependent.

$A$ coin is tossed three times. Let $A$ be the event of "getting three heads" and $B$ be the event of "getting a head on the first toss". Then $A$ and $B$ are

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