Question

1. A small company must decide whether to merge with a larger company to make more investments. If they merge and it is a good sales year, there will be a $840,000 profit; if they merge and it is a poor sales year, there will be a deficit of $ 260,000. If they do not merge and it is a good sales year there will be a $480,000 profit; if they do not merge and it is a poor sales year there will be a $52,000 profit. If the probability of a good sales year is 0.30 and the probability of a poor sales year is 0.70, what is the expected profit?

2. A coin is tossed 431 times. Use Binomial Distribution to approximate the probability of getting at most 235 tails.

Answer 1

solution 0 Let's tabulate the given data as zallows Do not image Groot Sales Yeah Merge Propit: $840,000 Progit. : $480,000 Sales Year Deficit : $260,000 Prezit: $.52,000 a → Probability fe good sales yeay pćGSY)=0-3 Probability. post sales year PC PSY) = 0.7 Asumption : símce nothing is mentioned about probability of morge probability of do not morge, considating do not and probability to of merge (81 that probability I am merge as 0-5 =0.5 P( Do not marge) P(Morge) sales Let's sind the good proşit when it is a yeal. Good Sales Year : Propit (651) Bragit (Morge) + Portal (Dont Marge)

Progit (GSY) Progit (Morge) + Prosit (Do not Mage) 1651) xP (Mange) 840,000 + [ PCG5Y) XP (po inst malige X480,000] Io. 0•3X0.5% 840,000 o]+[0.3x0:57 480000 $198,000 Similatej fetts zind propit when it is a pool Progit (GY) sales: Jeal. X Port Sales Yeall Prozit (PSY) = – Depicit (Marge) + Progit bo nät malige [F(psYjx P Menze) X 260,000 +[P(PSW) x P (Do not matige 52000 - [ 0.7x0.5x250pod] +L-7x0:5* 52000 72800 Negative sign indicates degiat. Hogiat (PSY) $12800

Now, expected prozit Proşit (659) -Degicit (PSY 118000 72800 $ 125,200 Answer 2) - A coin is tossed 431 times. We need to demine preşebility -gelling at most 235 tals. Probability of success CP Bobability & gothing tail when a comis tossed 0-5 P n Gel (HD) 1 P-0.5 221 Binomial distribiilion, P(X) qe number of skicesses n- number है- events / trials p- probability of suces We need to däərmine, PCX=235). @ n=431, p=0.5 gim online. Binomial calculator P(x= 235) Answal 0.97306