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Question

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 A 67
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)1P(T)P(¯¯¯4)=0.5×127=67

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