a Is it possible that she drew the same marble every time?
B
b Is it possible that she drew the same marble every time?
C
c Is it possible that she draws the same marble every time?
A
a No, see solution.
B
b No, see solution.
C
c Not possible.
Practice makes perfect
aProbability is calculated by dividing the number of marbles of a certain color by the total number of marbles.
P=Number of favorable outcomes/Number of possible outcomes
The exercise states that after picking a marble she puts it back in the bag. Therefore, not having recorded any red marbles does not mean that there are no red marbles in the bag.
b No, she cannot! Since she always puts back the marble she picked, each time she draws a marble the probability of drawing the same marble or any other marble that is not red will be the same. If there is one or more red marbles in the bag, it will be highly unlikely that she has not drawn a red marble after 100 picks. However, it will not be impossible.
c Just like in Part C, we cannot be absolutely certain that there are no red marbles no matter how many times we draw marbles. Given that red marbles are in the bag, each time we draw there will be a probability of drawing a marble that is another color.
