$($a$)$ If the probability that the rezoning will be approved is $0\mathrm{.}5,$ what decision is recommended?

purchase

do not purchase

What is the expected profit $($in dollars$)?$

$

possible resistance to the rezoning proposal from area residents. Probabilities are as follows.

Let

$H=$ High resistance to rezoning

$L=$ Low resistance to rezoning

$P(H)=0\mathrm{.}45,P(s_1|H)=0\mathrm{.}17,P(s_2|H)=0\mathrm{.}83$

$P(L)=0\mathrm{.}55,P(s_1|L)=0\mathrm{.}77,P(s_2|L)=0\mathrm{.}23$

What is the optimal decision strategy if the investor uses the option period to learn more about the resistance from area residents before making the purchase decision?

If high resistance $H_1{d}_2$ do not purchase. If low resistance $L,d_2$ do not purchase.

If high resistance $H_1{d}_2$ do not purchase. If low resistance $L_1{d}_1$ purchase.

If high resistance $H,d_1$ purchase. If low resistance $L,d_1$ purchase.

If high resistance $H_1{d}_1$ purchase. If low resistance $L,d_2$ do not purchase.

option?

The investor $---$ Select$---vv$ purchase this option, as the payoff of the investing in it is $---$ Select$---vv$$$10,000$ dollars. In general, the cost of the option can be$,$ at most, $

payoff to break even with its cost of investing in it$.$