When a firm is a target of a merger, its stock price usually goes up to a price

that is a little lower $($which accounts for the probability that the merger may

not go through$)$ than the bid price of the merger. If the merger does not go

through, the stock price of the target firm usually reverts back to its original

price.

Suppose that the bid price is $$150,$ the original price is $$100$ and the current

price is $$125$ and the riskless return is $1\mathrm{.}1.$

$1.$ What is the probability that the merger will go through?

$($a$)60\%$

$($b$)40\%$

$($c$)75\%$

$($d$)$ None of the above.

$2.$ What is the risk$-$neutral probability that the merger will go through?

$($a$)60\%$

$($b$)40\%$

$($c$)75\%$

$($d$)$ None of the above.

$3.$ What is the price for a bet that pays $$2\mathrm{.}2$ if the merger goes through and

$0$ otherwise.

$($a$)$ $$0\mathrm{.}75.$

$($b$)$ $$1.$

$($c$)$ $$1\mathrm{.}5.$

$($d$)$ $$2.$