If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the sum of the dice is $i$ ? Compute for all values of $i$ between $2$ and $12$

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If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the sum of the dice is $i$ ? Compute for all values of $i$ between $2$ and $12$

Accepted Answer

$\begin{aligned} P (A ∣ i = 2) = 0 \\ P (A ∣ i = 3) = 0 \\ P (A ∣ i = 4) = 0 \\ P (A ∣ i = 5) = 0 \\ P (A ∣ i = 6) = 0 \\ P (A ∣ i = 7) = \frac{1}{6} \\ P (A ∣ i = 8) = \frac{1}{5} \\ P (A ∣ i = 9) = \frac{1}{4} \\ P (A ∣ i = 10) = \frac{1}{3} \\ P (A ∣ i = 11) = \frac{1}{2} \\ P (A ∣ i = 12) = 1 \end{aligned}$

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If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the sum of the dice is $i$ ? Compute for all values of $i$ between $2$ and $12$

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A First Course in Probability

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If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the sum of the dice is i? Compute for all values of i between 2 and 12

Step by Step Solution

Step 1 : Given Information

Step 2 Calculation.

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If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the sum of the dice is $i$ ? Compute for all values of $i$ between $2$ and $12$