Please solve the math and show the evaluation and calculation.

$1.$ Consider a share of stock currently priced at $$30.$ The size of the possible price changes, and the probabilities of these changes occurring, are as follows:

Size of the up move: $1\mathrm{.}333,$ probability of up move: $55\%.$ Calculate the value of the PUT option on the stock with an exercise price of $$30.$