Question

P(n) models the probability, when rolling a pair of dice, of obtaining two numbers whose sum is n 2 6 7 P(n) 1/36 5/36 6/36 when does the probability increase faster? a)Between a sum of 2 and a sum of 6 b) Between a sum of 6 and a sum of 7 c)the probability increases at the same rate over both intervals

Answer 1

c)the probability increases at the same rate over both intervals

Step-by-step explanation:

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Answer 2

Option c.

Explanation:

From the given table, it is clear that

`P(2)=(1)/(36)`

`P(6)=(5)/(36)`

`P(7)=(6)/(36)`

The increasing rate of probability between a sum of 2 and a sum of 6 is

`r_1=(P(6)-P(2))/(6-2)`

`r_1=((5)/(36)-(1)/(36))/(4)=(1)/(36)`

The increasing rate of probability between a sum of 6 and a sum of 7 is

`r_2=(P(7)-P(6))/(7-1)`

`r_2=((6)/(36)-(5)/(36))/(1)=(1)/(36)`

Since
`r_1=r_2`, therefore the probability increases at the same rate over both intervals.

Hence, the correct option is c.