Respuesta :
Answer:
The probability is:
       [tex]\dfrac{9}{38}[/tex]
Step-by-step explanation:
We need to use the Baye's theorem in order to find the probability .
Jar 1: Â has 1 white ball and 4 black balls.
This means that the probability of white ball is: 1/5
( since there are a total of 1+4=5 balls out of which 1 is white)
Jar 2: has 2 white balls and 1 black ball.
This means that the probability of white ball is: 2/3
( since there are a total of 2+1=3 balls out of which 2 are white)
Jar 3 : has 3 white balls and 2 black balls.
This means that the probability of white ball is: 3/5
( since there are a total of 3+2=5 balls out of which 3 are white)
Hence, the probability the ball was drawn from Jar 1​, given that the ball is white is:
Ratio of drawing jar 1 and a white ball from it to the sum of choosing each jar and a white ball from it.
i.e.
[tex]=\dfrac{\dfrac{1}{2}\times \dfrac{1}{5}}{\dfrac{1}{2}\times \dfrac{1}{5}+\dfrac{1}{3}\times \dfrac{2}{3}+\dfrac{1}{6}\times \dfrac{3}{5}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{1}{10}+\dfrac{2}{9}+\dfrac{1}{10}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{2}{10}+\dfrac{2}{9}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{38}{90}}\\\\\\=\dfrac{9}{38}[/tex]
