Answer:
a
![P(N_g) = 0.5155](https://tex.z-dn.net/?f=P%28N_g%29%20%3D%200.5155)
b
![P(K ) = 0.36364](https://tex.z-dn.net/?f=P%28K%20%29%20%3D%200.36364)
c
Step-by-step explanation:
From the question we are told that
The number of green marbles in Urn 1 is ![N_g = 4](https://tex.z-dn.net/?f=N_g%20%20%3D%20%204)
The number of yellow marbles in Urn 1 is ![N_y = 5](https://tex.z-dn.net/?f=N_y%20%3D%205)
The number of green marbles in Urn 2 is ![n_g = 7](https://tex.z-dn.net/?f=n_g%20%3D%207)
The number of yellow marbles in Urn 1 is ![n_y = 4](https://tex.z-dn.net/?f=n_y%20%3D%204)
The probability of choosing Urn 1 is ![P(U1) = 0.63](https://tex.z-dn.net/?f=P%28U1%29%20%3D%200.63)
The probability of choosing Urn 2 is ![P(U2) = 1- 0.63 =0.37](https://tex.z-dn.net/?f=P%28U2%29%20%3D%201-%200.63%20%3D0.37)
Generally the total marble in Urn 1 is
![N_t = N_g +N_y](https://tex.z-dn.net/?f=N_t%20%3D%20N_g%20%2BN_y)
=>
=> ![N_t = 9](https://tex.z-dn.net/?f=N_t%20%3D%20%209)
Generally the total marble in Urn 2 is
![n_t = n_g +n_y](https://tex.z-dn.net/?f=n_t%20%3D%20n_g%20%2Bn_y)
=>
=> ![n_t = 11](https://tex.z-dn.net/?f=n_t%20%3D%20%2011)
Generally the probability of choosing green marble is
=>
=> ![P(N_g) = 0.5155](https://tex.z-dn.net/?f=P%28N_g%29%20%3D%200.5155)
Generally the probability that a yellow marble was chosen, if it is known that Urn 2 was chosen is mathematically represented as
![P(K ) = \frac{n_y}{n_t}](https://tex.z-dn.net/?f=P%28K%20%29%20%3D%20%5Cfrac%7Bn_y%7D%7Bn_t%7D)
=> ![P(K ) = \frac{4}{11}](https://tex.z-dn.net/?f=P%28K%20%29%20%3D%20%5Cfrac%7B4%7D%7B11%7D)
=> ![P(K ) = 0.36364](https://tex.z-dn.net/?f=P%28K%20%29%20%3D%200.36364)
Generally the probability of choosing yellow marble is
=>
=> ![P(N_y) = 0.4845](https://tex.z-dn.net/?f=P%28N_y%29%20%3D%200.4845)
Generally the probability that Urn 1 was chosen, if it is known that a yellow marble was drawn is mathematically represented as
![P(U1 | N_y ) = \frac{ P( U1 \ n N_y)}{P(N_y)}](https://tex.z-dn.net/?f=P%28U1%20%7C%20N_y%20%29%20%3D%20%5Cfrac%7B%20P%28%20U1%20%5C%20n%20%20N_y%29%7D%7BP%28N_y%29%7D)
=> ![P(U1 | N_y ) = \frac{0.63 * [\frac{5}{9} ] }{0.4845 }](https://tex.z-dn.net/?f=P%28U1%20%7C%20N_y%20%29%20%3D%20%5Cfrac%7B0.63%20%2A%20%5B%5Cfrac%7B5%7D%7B9%7D%20%5D%20%7D%7B0.4845%20%7D)
=>