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 1/3

B 2/3

C 2/5

D 4/15

Solution

Correct Answer: Option A

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 = \(P\left(\frac AB\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}=\frac{\displaystyle\frac28}{\displaystyle\frac68}=\frac13\)

Solution

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