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An experiment consists of flipping a coin and then flipping it a second time if head occurs. If a tail occurs on the first flip, then a six-faced die is tossed once. Assuming that the outcomes are equally likely, what is the probability of getting one head and one tail?
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The correct answer is:
$1 / 8$
Events when a coin is flipped and head occurs are $\{\mathrm{HT}, \mathrm{HH}\}$
Events when a coin is flipped and tail occurs are $\{\mathrm{T} 1$, $\mathrm{T} 2, \mathrm{~T} 3, \mathrm{~T} 4, \mathrm{~T} 5, \mathrm{~T} 6\}$
$(\because$ dice are rolled after tail appears) So, Total number of events $=8$ Favourable event $=\{\mathrm{H} \mathrm{T}\}=1$
$\therefore$ Required probability $=\frac{1}{8}$
Events when a coin is flipped and tail occurs are $\{\mathrm{T} 1$, $\mathrm{T} 2, \mathrm{~T} 3, \mathrm{~T} 4, \mathrm{~T} 5, \mathrm{~T} 6\}$
$(\because$ dice are rolled after tail appears) So, Total number of events $=8$ Favourable event $=\{\mathrm{H} \mathrm{T}\}=1$
$\therefore$ Required probability $=\frac{1}{8}$
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