Respuesta :
Answer: Our required probability is 0.642.
Step-by-step explanation:
Since we have given that
Probability of red candies from first bowl = 50% = 0.5
Probability of green candies from second bowl = 50% = 0.5
Let the probability of chosing first bowl be 'x'.
Let the probability of chosing second bowl be '1-x'
Probability of red candies from second bowl = 30% = 0.3
Probability of green candies from second bowl = 70% =0.7
Probability of red that comes from the first bowl = 75% = [tex]P(B_1|R)=0.75[/tex]
According to question,
[tex]P(B_1|R)=\dfrac{P(R|B_1).P(B_1)}{P(R|B_1).P(B_1)+P(R|B_2).P(B_2)}\\\\0.75=\dfrac{0.5x}{0.5x+0.3(1-x)}\\\\0.75=\dfrac{0.5x}{0.5x+0.3-0.3x}\\\\0.75=\dfrac{0.5x}{0.2x+0.3}\\\\0.75(0.2x+0.3)=0.5x\\\\0.15x+0.225=0.5x\\\\0.225=0.5x-0.15x\\\\0.225=0.35x\\\\\dfrac{0.225}{0.35}=x\\\\0.642=x[/tex]
Hence, our required probability is 0.642.
