Question

p(n) models the probability, when rolling a pair of dice, of obtaining two numbers whose sum is n. when does the probability increase faster? choose 1 answer: between a sum of 2 and a sum of 6 between a sum of 6 and a sum of 7 the probability increases at the same rate over both intervals

Explanation:

Step1: Calculate the rate of increase between 2 and 6

The change in probability is \(P(6)-P(2)=\frac{5}{36}-\frac{1}{36}=\frac{4}{36}\). The change in \(n\) is \(6 - 2=4\). The rate of increase is \(\frac{\frac{4}{36}}{4}=\frac{1}{36}\)

Step2: Calculate the rate of increase between 6 and 7

The change in probability is \(P(7)-P(6)=\frac{6}{36}-\frac{5}{36}=\frac{1}{36}\). The change in \(n\) is \(7 - 6 = 1\). The rate of increase is \(\frac{\frac{1}{36}}{1}=\frac{1}{36}\)

Answer:

The probability increases at the same rate over both intervals