A man alternatively tosses a coin and throws a die. The probability of getting a head on the coin before he gets 4 on the die is
A
67
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B
23
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C
34
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D
12
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Solution
The correct option is A67 Let the desired event be called E then P(E)=P(H)+P(T)P(¯¯¯4)P(H)+P(T)P(¯¯¯4)P(T)P(¯¯¯4)P(H)+.............∞ where P(¯¯¯4)=56,P(H)=P(T)=0.5 thus we can see that an G.P sum is formed with first term =P(H) and common ratio =P(T)P(¯¯¯4) hence P(E)=P(H)1−P(T)P(¯¯¯4)=0.5×127=67