The correct answer is Option B: 5.
To solve this problem, we need to determine how many times the ball hits the ground before it stops bouncing. The ball is initially dropped from a height of 1.5 meters and each time it bounces, it reaches 4/5th of the previous height. The ball stops bouncing when the height is less than 50 cm (0.5 meters).
     Let's calculate the height after each bounce:
     ● First Bounce:  
           ○ Initial height = 1.5 meters
           ○ Height after first bounce = \( \frac{4}{5} \times 1.5 = 1.2 \) meters
     ● Second Bounce:  
           ○ Height after second bounce = \( \frac{4}{5} \times 1.2 = 0.96 \) meters
     ● Third Bounce:  
           ○ Height after third bounce = \( \frac{4}{5} \times 0.96 = 0.768 \) meters
     ● Fourth Bounce:  
           ○ Height after fourth bounce = \( \frac{4}{5} \times 0.768 = 0.6144 \) meters
     ● Fifth Bounce:  
           ○ Height after fifth bounce = \( \frac{4}{5} \times 0.6144 = 0.49152 \) meters
     After the fifth bounce, the height is approximately 0.49152 meters, which is less than 0.5 meters. Therefore, the ball will not bounce again after the fifth hit.
     Thus, the ball hits the ground 5 times before it stops bouncing.