Answer: The probability of selecting either a lime or bubble gum followed by a papaya is 425/2209
Step-by-step explanation:
 Since, there are four types of items in the jar, namely- lime, papaya, mango and bubble gum that have quantities of 12, 17, 5 and 13 respectively. Before finding the probabilities, we first add up the quantities or number of different items in the jar.
 12 + 17 + 5 + 13 = 47 in total.
 Since lime is 12 in number, the probability of selecting a lime is = 12/47.
 Bubble gums are 13 in number, so the probability of selecting a bubble gum = 13/47. 
 Then the probability of selecting either a lime or a bubble gum is the addition of the probabilities of selecting a lime and selecting a bubble gum:
 = 12/47 + 13/47
 = 25/47.
 Again, the probability of selecting a papaya is = 
 number of papaya/total number of items
 = 17/47
 If the system is with replacement, then the probability of selecting a lime or bubble gum followed by a papaya is:
 = Probability of selecting a lime or bubble gum × Probability of selecting papaya
 = 25/47 × 17/47
 = 425/2209
 
 The probability of selecting a lime or bubble gum followed by a papaya is 425/2209