Twelve of the last 16 winners of the school science fair have been seventh grade students. Mona placed 3 red marbles and 1 green marble in a bag to create a simulation to predict whether future science fair winners will be seventh graders. According to Mona’s model, what is the probability that the next 4 winners will all be seventh grade students?

StartFraction 3 over 16 EndFraction

StartFraction 81 over 256 EndFraction

Three-fourths

StartFraction 7 over 8 EndFraction

, 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

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