Question

question 86 of 100
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

The first die shows 6. Let the value of the second die be \(x\). The sum of the two dice is \(S=6 + x\). We want \(S>9\), so \(6+x>9\), which simplifies to \(x > 3\).

Step2: Calculate the probability

A die has 6 possible outcomes (\(x = 1,2,3,4,5,6\)). The values of \(x\) that satisfy \(x>3\) are \(x = 4,5,6\). The number of favorable outcomes \(n = 3\), and the total number of outcomes \(N=6\). The probability \(P=\frac{n}{N}\).

Answer:

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