Final answer:
The question seems to have typos, making it unclear; however, it appears to involve algebraic simplification of fractions and probability. Without the correct information, it is not possible to simplify the expression or solve for specific values of p and q. Additionally, there is a mention of a physics concept regarding the ratio of point charges based on the number of electric field lines.
Step-by-step explanation:
The original algebraic expression provided in the question is somewhat unclear due to possible typos and missing context. However, it seems to be a fractional expression involving products and quotients of binomials, and possibly a simplification problem involving algebraic fractions. Without the correct expression, it is not possible to provide a step-by-step simplification process. To find specific values of p and q, we often need a system of equations or a specific equation where we can substitute given values and solve for the unknowns. When dealing with probabilities, as touched upon within the question, we typically use the fact that the sum of all probabilities must equal 1, using expressions like p + q = 1. For the example involving dice rolls, the probability question can be tackled using the complement rule and considering independent events.
The ratio of point charges question involving electric field lines seems to be a physics question about the relationship between the quantity of field lines and the magnitude of the charges. This question seems to be tied to a principle that correlates the number of field lines with the charge's strength, and it suggests finding a ratio of these charges.