Alice and Bob are playing a game. Alice starts first. On Alice's turn, she flips a coin. If she gets a heads, she wins. If not, it becomes Bob's turn. On Bob's turn, he flips a coin. If he gets a tails, he wins. If not, it becomes Alice's turn. What is the probability that Alice wins the game?

Answer:The probability that Alice wins the game=[tex]\frac{1}{2}[/tex]Step-by-step explanation:We are given that Alice and Bob are playing a game .We have to find the probability that Alice wins the game .If Alice win when she gets head and lose when she gets tail.Bob wins when she gets tail and she lose when she gets head.Total results in a coin=Head, tail=2Number of head in a coin=1Number of tail in a coin= 1Probability is defined as the possibility of an event that occurred[tex]P(E)=\frac{Number\;of\;favourable\;cases}{total\;of\;cases}[/tex]The probability that Alice wins the game=[tex]\frac{Number\;of\;favourable\;cases}{Total\;number\;of\;cases}[/tex]The probability that Alice wins the game=[tex]\frac{number \;of \;heads}{Total\; results}[/tex]The probability that Alice wins the game=[tex]\frac{1}{2}[/tex]