Final answer:
The probability that both pieces of bubble gum picked are grape flavored is 3/38, calculated by multiplying the probability of picking a grape piece first (6/20) and then another after the first is given away (5/19).
Step-by-step explanation:
The question asks us to calculate the probability that both pieces of bubble gum picked from the bag are grape flavored. The bag contains six grape, nine sour apple, and five regular flavored pieces. To find the probability that both pieces are grape, we calculate the probability of picking one grape piece and then another grape piece after the first has been given away.
The total number of pieces initially is 6 (grape) + 9 (sour apple) + 5 (regular) = 20 pieces. The probability of picking a grape piece first is 6/20. After giving it away, there are 5 grape pieces left and the total number of pieces in the bag is now 19. The probability of then picking another grape piece is 5/19. To find the overall probability of both events occurring, we multiply the individual probabilities: (6/20) * (5/19) = 30/380 = 3/38.
Therefore, the probability that both pieces are grape is 3/38.