A certain stake is to be won by the first person who throws an ace with an octahedral die, if there are $4$ persons what is the chance of the last to win the stake?

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Solution

Person $⟶ A, B, C, D$
Win probability $= \frac{1}{8} A^{^{'}} = \frac{1}{8}$
Loss probability $= \frac{7}{8} B^{^{'}} = \frac{7}{8}$
$C^{^{'}} = \frac{7}{8}$
$D = \frac{1}{8}$ chance of D
$\frac{7}{8} \times \frac{7}{8} \times \frac{7}{8} \times \frac{1}{8}$
Required probability $= {(\frac{7}{8})}^{3} \times \frac{1}{8}$

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A certain stake is to be won by the first person who throws an ace with an octahedral die, if there are 4 persons what is the chance of the last to win the stake?

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A certain stake is to be won by the first person who throws an ace with an octahedral die, if there are $4$ persons what is the chance of the last to win the stake?