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
The probability that the next 4 winners will all be seventh grade students can be calculated as the probability of selecting a seventh grade student from the bag 4 times in a row.
The probability of selecting a seventh grade student from the bag is 3/4 (3 red marbles out of 4 total marbles).
Therefore, the probability of selecting a seventh grade student 4 times in a row is:
(3/4) * (3/4) * (3/4) * (3/4) = (81/256)
So, according to Mona's model, the probability that the next 4 winners will all be seventh grade students is StartFraction 81 over 256 EndFraction.