A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

Let us solve this question one step at a time.

We know that each time the ball is dropped it bounces
back and reach 2/3 of the height.

Thus, after the first bounce, the ball will reach 2/3
of the height from which it was dropped.

After the second bounce, the ball will reach 2/3 of
the height again after the first bounce.

Thus the total height at which the ball must have
reached by this time will be 2/3 * 2/3 = 4/9 of the original height.

After third bounce, 2/3 * 2/3 * 2/3 = 8/27 of the
original height.

After fourth bounce, 2/3 * 2/3 * 2/3 * 2/3 = 16/81 of
the original height.

Thus, the ball will reach 16/81 of the original
height from which it was dropped.