Two standard 6 sided dice are rolled. One is purple and one is green. What is the probability that sum of the two dice on a roll is 7 given that the purple die for that roll landed on 6?

P(Sum of the dice is 7 | Purple Die Landed on 6)

1/6

Step-by-step explanation:

As the purple die has already rolled and the number landed is 6, to find the probability of the sum of the dice being 7, there is only one option for the yellow die:

purple result + yellow result = 7

6 + yellow result = 7

yellow result = 1

So the yellow die needs to roll a 1, over a total of 6 possibilities, so the probability is 1/6

it's

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for