Question

Three hats each contain ten coins. Hat 1 contains two gold coins, five silver coins and 2 contains four gold coins and six silver coins. Hat 3 contains olour of each of the three selected coins. List the three copper coins. Hat three gold coins and seven copper coins. We randomly select one coin f and seven copper coins. We randomly select one coin from each hat (a) The outcome of interest is the complete sample space of outcomes and calculate the probability of each (b) Let X be the number of gold coins selected. Find the probability distribution of X

Answer 1

Solution(a)

Total No. Of sample space = 3×2×2= 12

Sample space with probability is

(Gold, Gold, Gold) =(2×4×3/(10×10×10))= 0.024

(Gold, Silver, Gold)=(2×6×3)/1000 = 36/1000= 0.036

(Gold, Gold, Copper)=(2×4×7)/1000=0.056

(Gold, silver, copper)=(2×6×7)/1000=84/1000=0.084

(Silver, Gold, Gold)=(5*4*3)/1000=0.060

(Silver, Gold, Copper)=(5×4×7)/1000=0.14

(Silver,Silver, Gold)=(5×6×3)/1000=0.09

(Silver, silver, copper)=(5×6×7)/1000=0.21

(Copper, Gold,Gold)=(3×4×3)/1000=0.036

(Copper, Gold, Copper)=(3×4×7)/1000=0.084

(Copper, silver,Gold)=(3×6×3)/1000=0.054

(Copper, silver, copper) = (3×6×7)/1000= 0.126

Solution(b)

P(X= No gold coin selected) = 0.126+0.21= 0.336

P(1 Gold coin selected) = 0.054+0.084+0.09+0.14+0.084= 0.452

P(2Gold coin selexted)= 0.036+0.06+0.056+0.036=0.188

P(3 Gold coin)= 0.024