trading atNOTE: ASSUME Ris free rate of $0$; $252$ trading days in a year; and Normal distribution for all questions. $($best to solve by hand$)$

Q$2.$ Option Pricing $(20$ points$)$

Underlying currently tradingat $5200.$ Put option with strike at $5275$ has one week left before expiration. Put option has an annual IV of $$600.$

Q$2$a$.$ What is the probability for PUT to expire in the money?

Q$2$b$.$ What is the average price of the underlying at expiration conditional on PUT expiring ITM?

Q$2$c$.$ Based on Q$2$a$,$ and Q$2$b$,$ how much should the PUT be priced at today?

Q$2$d$.$ Out of total call price from Q$2$c$,$ how much is time value and how much is intrinsic value?