Asemiconductor wafer fabrication facility received an order for specially designed pro$-$ totype semiconductor wafers. The cost of producing each wafer is estimated to be $$20,000.$ The customer agrees to pay $$150,000$ for three good wafers, $$200,000$ for four good wafers, and $$250,000$ for five good wafers. Other than the three, four, or five good wafers, al other wafers, good or bad, must be destroyed. To obtain the contract, the wafer fab offers to pay the customer $$100,000$ fi at least three good wafers are not produced. Each wafer is produced independently; the probability of a wafer being ac$-$ ceptable si estimated to be $0\mathrm{.}75.$ Determine the number of wafers to produce, as wel as the probability of losing money on the transaction.