Could use help going through this problem step by step! thank you in advance! 3.

Question

Could use help going through this problem step by step! thank you in advance!

3.33 A chest has 3 drawers: the first drawer (D) has 2 silver coins (S), the second drawer (D2) has 1 silver (S) and 1 gold (G) coin, and the thrid drawer (D3) has 2 gold (G) coins. A drawer is randomly selected and a coin is randomly selected from the chosen drawer. Lets (a) Use the law of total probability to determine the probability that the first coin selected from the drawer is gold, i.e. find P(G1) (b) Find the probability that both coins in the selected drawer are gold, i.e. find P(G1 and G2). This one is easy. Both coins are gold only if we are selecting from Ds, hence P(Gi and G2) -P(Ds) (c) Given that the selected coin is gold, determine the probability that other coin in the drawer is also gold, i.e. find P(G2lGi). Briefly interpret your result

Explanation / Answer

a) P(G1) =P(D1)*P(G1|D1)+P(D2)*P(G1|D2)+P(D3)*P(G1|D3) =(1/3)*0+(1/3)*(1/2)+(1/3)*1=1/2=0.5

b)P(G1 and G2) =P(D3) =1/3

c)P(G2|G1) =P(G2 and G1)/P(G1) =(1/3)/(1/2) =2/3

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