Question

1. you roll a pair of dice. if the first die shows a 6, what is the probability that the sum of the dice is greater than 9? (a) \\( \frac { 1 } { 6 } \\) (b) \\( \frac { 1 } { 3 } \\) (c) \\( \frac { 1 } { 2 } \\) (d) \\( \frac { 2 } { 3 } \\)

Explanation:

Step1: Determine the possible values of the second die

Since the first die shows 6, let the value of the second die be \(x\). We want \(6 + x>9\), which simplifies to \(x > 3\). The possible values of a die are \(1,2,3,4,5,6\). So \(x\) can be \(4,5,6\).

Step2: Calculate the probability

The total number of possible outcomes for a single die is \(n = 6\). The number of favorable outcomes ( \(x=4,5,6\)) is \(m = 3\). Using the probability formula \(P=\frac{m}{n}\), we have \(P=\frac{3}{6}=\frac{1}{2}\).

Answer:

D. \(\frac{1}{2}\)