TD - European calls and puts, a straddle and a butterfly spread

Question
In the question YOU MAY ASSUME
(i) that all Calls and Puts are of European type,
(ii) that (whether bought long or short) all Calls may be purchased for a
constant value C and all Puts may be purchased for a constant value
P,
(iii) that all calculations are to be made from the point of view of the holder
of the option (rather than that of the writer).
(a) A STRADDLE is an option strategy that consists of a position where
one is a long one Call and long one Put, both with same strike E and
expiry T. At expiry the underlying has a value S(T). What conditions
must S(T) satisfy in order for a straddle to be profitable?
Draw a profit diagram for a straddle, plotting the profit at expiry
against S(T). If an investor buys a straddle, what view is she or he
taking of the likely behaviour of the underlying?
(b) A BUTTERFLY SPREAD is an option strategy that consists of a position where one is long one Call with a strike E − K, long one call with
a strike E + K and short two calls, both with strike E, where the constant K satisfies 4C < K < E. All Calls are assumed to have the same
expiry T. At expiry the underlying has a value S(T). What conditions
must S(T) satisfy in order for a butterfly spread to be profitable?
Draw a profit diagram for a butterfly spread, plotting the profit at
expiry against S(T). If an investor buys a butterfly spread, what view
is she or he taking of the likely behaviour of the underlying?