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A coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed. If 8 possible outcomes are equally likely. Find the probability that the die shows a number greater than 4, if it is known that the first throw of the coin results in a tail

A coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed. If 8 possible outcomes are equally likely. Find the probability that the die shows a number greater than 4, if it is known that the first throw of the coin results in a tail Correct Answer 1\/3

Here Sample space S = { HH, HT, T1, T2, T3, T4, T5, T6 }

 

Let A be the event that the die shows a number greater than 4 and B be the event that the first throw of the coin results in a tail then,

 

 A = { T5, T6 }

 

 B = { T1, T2, T3, T4, T5, T6 }

 

Therefore, Required probability = PAB=PA∩BPB=2868=13

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