Explain the problem of induction- Discuss two different solutions to it.

The problem of induction is the philosophical issue of whether using induction to justify our beliefs is reasonable. We have memories and experience from past events that allow us to prepare for the future. Although the future is not certain, using generalizations and predictions, we can assume with some certainty that, what will happen tomorrow, will be similar, if not the same as what happened today. We use induction to predict events happening in the future or make generalizations based on previous information we have obtained for example, we can assume that during the day, the sun will pass over the sky and disappear at night. We can assume this because it has happened every day that we have cared to notice since we existed. We also make generalizations, for example, every spider I have seen had exactly eight legs, and therefore I can say that the next spider I see will have eight legs also.   The conclusions of the above arguments arrived due to inductive reasoning but they do not necessarily have the same degree of certainty as the premises.
Some spiders may carry a certain gene that when bred with a spider with a similar gene, may produce a six legged spider. Although the likely hood of that happening may be low, it is possible and therefore makes the argument invalid.
Making a series of observations, however many, may be thought to imply a particular conclusion about some future event only if induction itself works. If a prediction turns out to be correct, it does not establish the reliability of induction, except inductively.
How can a prediction or a conclusion to an inductive argument be justified?
David Hume (1711-1776, cited in Sober, 2004) states that there is a missing premise in all inductive arguments.

Inductive arguments take the form of

Observation (1) in my experience, fires are hot
Conclusion (2) therefore, all fires are hot

Hume states that... [continues]

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