Supposing there are 2 Jars.The first Jar has 9 green sweets and 5 purple sweets.

Question

Supposing there are 2 Jars.The first Jar has 9 green sweets and 5 purple sweets.The second Jar has 6 green sweets and 7 pink sweets.2 Jars have same probability of being chosen. a)Suppose we pick a sweet out of random.What is the probability it is a green sweet. b)supposing we pick 3 sweets from each of the Jars.Find the probability there are 3 green sweets picked out of the 6 sweets picked. c)Repeating it again we found 3 green Sweets picked out of the 6.Find the probability one of these 3 green sweets picked is from Jar 1.

Explanation / Answer

a) P(green sweet) = P(jar 1 and green) + P(jar 2 and green)

= (1/2)x(9/14) + (1/2)x(6/13)

= 0.5522

b) 3 green sweets can be picked in the following ways

P(all 3 green from jar 1 and no green from jar 2) = (9C3/14C3) x (7C3/13C3)

= 0.0282

P(2 green from jar 1 and 1 green from jar 2) = (9C2 x 5C1 / 14C3) x (6C1 x 7C2/13C3)

= 0.2179

P(1 green from jar 1 and 2 green from jar 2) = (9C1 x 5C2 / 14C3) x (6C2 x 7C1/13C3)

= 0.0908

P(3 green from jar 2 and no green from jar 1) = 5C3/14C3 x 6C3/13C3

= 0.0019

P(3 green out of 6 chosen) = 0.0282 + 0.2179 + 0.0908 + 0.0019 = 0.3388

c) P(one of the green swwets is picked from jar 1) = P(1 green from jar 1 and 2 green from jar 2) / P(3 green)

= 0.0908/0.3388

= 0.2680

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